WEB  STRESSES 

IN  REINFORCED  CONCRETE  BEAMS 

BY 


SABRO  UCHIMURA 

Ko-Gaku-Shi  Imperial  University,  Japan,  1920 


THESIS 

SUBMITTED  IN  PARTIAL  FULFILLMENT  OF  THE  REQUIREMENTS 
FOR  THE  DEGREE  OF  MASTER  OF  SCIENCE 
IN  THEORETICAL  AND  APPLIED  MECHANICS 
IN  THE  GRADUATE  SCHOOL  OF  THE  UNIVERSITY 
OF  ILLINOIS,  1922 


URBANA,  ILLINOIS 


Digitized  by  the  Internet  Archive 
in  2015 


https://archive.org/details/webstressesinreiOOuchi 


I <J  (■*--  t-V- 

"\ajlv  i; 


UNIVERSITY  OF  ILLINOIS 


THE  GRADUATE  SCHOOL 


June  3,  192 2 


i HEREBY  RECOMMEND  THAT  THE  THESIS  PREPARED  UNDER  MY 


SUPERVISION  BY SABRO  UCHILIURA 


ENTITLED  WEB  STRESSES  IB  REINFORCED  CONCRETE  BEAMS 


BE  ACCEPTED  AS  FULFILLING  THIS  PART  OF  THE  REQUIREMENTS  FOR 

THE  DEGREE  OF  MASTER  OF  SCIENCE  IN  THEORETICAL  AND  APPLIED 

MECHANICS 


JnjCharge  of  Thesis 


Recommendation  concurred  in* 


Head  of  Department 


Committee 


on 


Final  Examination* 


•Required  for  doctor’s  degree  but  not  for  master’s 


/'  ■ -PPOfS 


1 


TABLE  OF  CONTENTS 

I.  INTRODUCTION 

Page  No. 

1.  Preliminary 1 

2.  Scope  of  Investigation 2 

3.  Acknowledgments 3 

4.  Analysis  or  Theory. 4 

A.  Beams  Without  Web  Reinforcement 4 

B.  Action  of  Vertical  Stirrups 7 

C.  Beams  with  Bars  Bent  Up 9 

D.  Action  of  Bent-Up  Bar......... 11 

E.  Tee-Beams 12 

II.  Materials,  Test  Pieces,  Apparatus  and 
Methods  of  Testing 

5*  Materials 15 

6.  Test  Beams 21 

7.  Making  of  the  Beams 22 

8.  Storage  of  Specimens........ 26 

9.  Method  of  Testing. 26 


II 


III.  EXPERIMENTAL  DATA  AND  DISCUSSION 

Page 

No. 

10.  Description  of  Figures  .Photographs  and  Tables 34 

11.  Deflection  of  Beams 35 

A*  Beams  Without  Web  Reinforcement 

12.  Note  of  Tests 36 

a.  Beams  without  Hooks 36 

b.  Beams  with  Hooks..... 37 

13.  Beams  Without  Web  Reinforcement 39 

14.  Effect  of  Hooks  at  the  Ends  of  Beams 40 

15.  Position  of  the  Neutral  Axis 41 

16.  Value  of  Vertical  Shearing  Stress.... 43 

17.  Direction  of  the  Diagonal  Cracks. 46 

B.  Rectangular  Beams  with  Vertical  Stirrups 46 

18.  Note  of  Tests 46 

a.  Rectangular  Beam  with  4 in.  Spacing  of 

Stirrups 46 

b.  Rectangular  Beams  with  7 in.  Spacing  of 

Stirrups 50 

c.  Rectangular  Beams  with  11  in.  Spacing  of 

Stirrups. 51 

19.  Rectangular  Beams  with  Vertical  Stirrups 52 

20.  Stress  in  Stirrups... ••••  54 

21.  Effect  of  Spacing  of  the  Stirrups 55 

22.  Effectiveness  of  Vertical  Stirrups 57 


Ill 


Page 

No. 


C.  Tee-Beams  with  Vertical  Stirrups 59 

23.  Note  of  Test 59 

a.  Tee-Beams  with  4-in.  Spacing 59 

h.  Tee-Beams  with  7 in.  Spacing 60 

c.  Tee-Beams  with  11  in.  Spacing 62 

24.  Tee-Shaped  Beam  with  Vertical  Stirrups 64 

25.  Stress  in  Stirrups 66 

26.  Position  of  Neutral  Axis 68 

27.  Effect  of  Spacing  of  Stirrup 69 

I).  Rectangular  Beam  with  Bent-up  Bars 72 

28.  Note  of  Test... 72 

29.  Rectangular  Beams  with  Bent-Up  Bars 73 

30.  Conclusions 75 


IV 


LIST  OF  TABLES 

Page 

Table  1.  Tension  of  Steel 16 

Table  2.  Tests  of  Cement  and  Mortar 16 

Table  3.  Mechanical  Analysis  of  Sand 17 

Table  4.  Mechanical  Analysis  of  Gravel 18 

Table  5.  Physical  Properties  of  Concrete 20 

Table  6.  Spacing  and  Size  of  Vertical  Stirrups 22 

Table  7.  Strain  Gage  Constants  27 

Table  8,  Value  of  k and  j when  n = 7 and  p = 0,0233 42 

Table  9,  Calculated  Shearing  Stresses  46 

Table  10. Location  of  Crack  Openings  and  Their  Inclina- 
tion  47 

Table  11. Maximum  Unit  Stress  and  Total  Stress  in  the 

Stirrups  at  the  Load  of  200  000  lbs 55 

Table  12. Ratio  Between  Observed  and  Calculated 

Stirrup  Stress 57 

Table  13. Maximum  Unit  Stress  and  Total  Stress  in  the 

Stirrups  at  the  Load  of  200  000  lbs 67 

Table  14. Location  of  the  Neutral  Axis  in  T-Beams 69 

Table  15. Value  of  k and  3 in  T-Beams..... 69 

Table  16. Maximum  Observed  and  Calculated  Stresses  in 

the  Stirrups  at  the  Load  of  200  000  lb....  71 


V 


LIST  OP  PHOTOGRAPHS 


Page 

1.  View  of  Form  and  Reinforcement  for  Rectangular  Beams...,  23 


2.  View  of  Form  and  Reinforcement  for  T-Beams 24 

3.  View  of  Test  Beams 25 

4.  General  Apparatus  for  Tests 28 

5.  Preparation  of  Beams  for  Testing. 29 

6.  Strain  Gages... 31 

7.  Application  of  Strain  Gage  in  Testing 32 

8.  View  of  Beam  Ho. 221-1  at  Failure 79 

9.  View  of  Beam  Ho. 222-1  at  Failure 80 

10.  View  of  Beam  Ho. 223-1  at  Failure 81 

11.  View  of  Beam  Ho. 224-1  at  Failure..... 82 

12.  View  of  Beam  Ho.  225-1  at  Failure 83 

13.  Beam  Ho.  221-1  W 84 

14.  Beam  Ho.  221-1  E 84 

15.  Beam  Ho.  221-1  W 85 

16.  Beam  Ho.  221-1  E 85 

17.  Beam  Ho.  222-1  W 86 

18.  Beam  Ho.  222-1  E 86 

19.  Beam  Ho.  222-2  W 87 

20.  Beam  Ho.  222-2  E 87 

21.  Beam  Ho. 223-1  W 88 

22.  Beam  Ho.  223-1  E 88 

23.  Beam  Ho.  223-2  89 

24.  Beam  Ho.  223-2  E 89 

25.  Beam  Ho.  224-1  W . 90 

26.  Beam  Ho.  224-1  90 


VI 


Page 

27.  Beam  No.  224-2  W 91 

28.  Beam  No.  224-2  E 91 

29.  Beam  No.  225-1  W 92 

30.  Beam  No.  225-1  E 92 

31.  Beam  No.  225-2  W 93 

32.  Beam  No.  225-2  E 93 

33.  Beam  No.  226-1  W 94 

34.  Beam  No.  226-1  E 94 

35.  Beam  No.  22  6-2  W 95 

36.  Beam  No.  226-2  E 95 

37.  Beam  No.  22  7-1  W 96 

38.  Beam  No.  227-1  E 96 

39.  Beam  No.  227-2  W 97 

40.  Beam  No.  22  7-2  E 97 

41.  Beam  No.  228-1  W 98 

42.  Beam  No.  228-1  E 98 

43.  Beam  No.  228-2  W 99 

44.  Beam  No.  228-2  E 99 

45.  Beam  No.  229-1  W 100 

46.  Beam  No.  229-1  E 100 

47.  Beam  No.  229-2  W 101 

48.  Beam  No.  229-2  E ••••••• 101 


I.  INTRODUCTION 


I.  INTRODUCTION 

1.  Preliminary, - In  a reinforced  concrete  beam 
having  a depth  relatively  large  in  comparison  with  its  length 
the  resistance  to  web  stresses  becomes  very  important,  and 
diagonal  tension  and  bond  stresses  may  control  the  strength 
of  the  beam.  At  the  present  time,  there  is  a considerable 
amount  of  information  available  concerning  the  resistance 
of  web  reinforcement  to  the  strains  due  to  diagonal  tension, 
but  conclusive  data  are  still  lacking  on  a number  of  questions 
such  as  the  action  of  stirrups  in  deep  beams  and  T-beams, 

High  diagonal  tensile  stresses  are  developed  when 
the  vertical  shear  is  large  in  comparison  with  the  bending 
moment:  this  condition  is  found  in  short,  deep  beams.  Tests 

by  W.  A,  Slater  for  the  Emergency  Fleet  Corporation  in  1918 
showed  that  where  such  high  web  stresses  occurred  they  could 
be  resisted  by  properly  designed  web  reinforcement,  and 
extremely  high  shearing  unit  stresses  were  developed  in  the 
tests,  which  included  beams  of  both  rectangular  and  I-section, 

As  a result  of  this  investigation  the  recent  proposed  specifica- 
tions of  the  American  Concrete  Institute  and  of  the  Joint 
Committee  on  Concrete  and  Reinforced  Concrete  allow  a maximum 
shearing  unit  stress  in  reinforced  concrete  beams  of  twelve 
hundredths  of  the  ultimate  compressive  strength  of  the  concrete, 
nearly  twice  as  high  a value  as  has  been  permitted  in  previous 
specifications.  Tests  to  determine  whether  such  high  web 
stresses  may  be  developed  in  the  commoner  forms  of  beams  are  tnus 
of  timely  interest. 


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Theoretical  analysis  of  the  stress  in  beams  may 
be  applied  to  some  extent  to  the  problem;  however,  it  seems 
likely  that  the  short,  deep  beam  does  not  follow  the  same 
law  of  action  as  the  ideal  slender  one,  especially  with 
regard  to  the  distribution  of  bearing  stresses  and  so-called 
arch  action.  The  tests  described  in  this  thesis  were,  there- 
fore, made  to  supplement  the  theoretical  indications  with 
actual  observations  of  the  behaviour  of  full-sized  test  pieces. 
The  tests  form  a part  of  the  investigation  of  web  stresses  in 
reinforced  concrete  beams  which  has  been  carried  on  at  the 
University  of  Illinois  under  the  direction  of  Professor  A.  U. 
Talbot  during  the  last  fifteen  years. 

2.  Scope  of  Investigation.-  The  investigation 
was  planned  to  study  the  effect  of  stirrup  spacing  in  deep 
beams,  to  compare  the  web  resistance  of  beams  of  rectangular 
section  and  T-sections,  and  to  determine  limiting  values  of 
shearing  stress  which  may  be  developed. 

The  tests  were  made  on  (1)  two  types  of  rectangular 
beams  without  web  reinforcement,  (2)  three  types  of  rectangular 
sections  and  three  types  of  T-sections,  with  loose  vertical 
stirrups,  and  (3)  one  type  of  beam  with  reinforcing  bars  bent 
up  in  the  outer  thirds  of  the  span.  Two  companion  beams  were 
made  of  each  type. 

For  longitudinal  reinforcement,  each  beam  had  four 
high  carbon  steel  corrugated  bars.  The  diameter  of  the  bars 

l H 

was  i l/4:  in.  and  the  sectional  area  was  one  square  inch, 
making  the  percentage  of  reinforcement  2.33  per  cent. 


3 

The  diameters  of  stirrups  for  the  various  spacings 
were  designed  to  produce  practically  the  same  theoretical 
stress  in  the  web  reinforcement  of  different  beams  at  a 
given  load* 

All  beams  were  made  of  1:2:4  concrete*  Most  of 
them  were  tested  at  the  age  of  from  60  to  62  days*  Control 
cylinders  were  made  with  all  beams.  The  beams  were  tested 
by  applying  load  in  a testing  machine  and  measuring  a large 
number  of  sticdns  in  longitudinal  and  web  steel  and  in  the 
concrete*  These  measurements  were  made  by  the  use  of  the 
Berry  strain  gage.  Deflections  were  also  measured  and  the 
position  and  size  of  cracks  was  carefully  observed  throughout 
the  test.  The  load  was  increased  in  regular  increments  until 
the  beam  failed,  and  a complete  set  of  observations  was  made 
after  each  increment  of  load  was  applied. 

3*  Acknowl  e dgment  * - These  tests  were  made  as  part 
of  the  research  work  of  the  Engineering  Experiment  Station  of 
the  University  of  Illinois  under  the  general  directions  of 
Professor  A*  N.  Talbot.  The  specimens  were  made  under  the 
supervision  of  Professor  F.  E.  Richart  of  the  Engineering 
Experiment  Station.  Mr.  R.  1.  Brown,  Research  Assistant 
in  the  same  station  gave  many  helpful  suggestions  and  much 
valuable  assistance  both  in  making  the  tests  and  in  working 
up  the  data.  Mr.  If.  B.  Green,  Research  Graduate  Assistant 
in  Theoretical  and  Applied  Mechanics  assisted  in  making  the 
tests.  To  these  people  the  writer  expresses  appreciation  for 
the  assistance  rendered. 


4 


4,  Analysis  or  Theory, - 

A*  Beams  Without  Web  Reinforcement,-  In  a simply 
supported  reinforced  concrete  beam  under  loads,  there  are 
tensile  strains  on  the  convex  side  and  compressive  strains 
on  the  concave  side,  and  diagonal  tensile  strains  in  the  web 
of  the  beam  between  support  and  load  point,  For  use  in 
finding  the  s tress  at  the  top  of  the  beam  the  assumption  that 
an  initial  plane  section  remains  plane  under  flexure  may  be 
allowed  without  any  practical  objection,  and  if  the  stress 
strain  relations  found  from  cylinder  tests  are  used  to  modify 
the  variation  of  stress  in  the  beam,  a satisfactory  analysis 
of  the  compressive  stresses  in  concrete  may  be  made. 

The  tensile  strength  of  concrete  is  very  small, 
perhaps  one-tenth  of  the  compressive  strength,  so  that  at 
ordinary  working  stresses  in  beams  the  concrete  has  failed 
at  many  places  in  tension.  Tests  show  that  as  the  loads  are 
increased  on  a beam,  the  reinforcing  steel  develops  an 
increasing  proportion  of  the  resisting  moment,  until  at  the 
ultimate  load  it  furnishes  the  entire  tensile  resistance  of 
the  beam.  For  most  purposes,  therefore,  the  assumption  of 
no  tensile  resistance  in  the  concrete  is  a satisfactory  one, 
and  errs,  of  course,  on  the  side  of  safety. 

The  web  stresses  in  a beam  having  no  web  reinforce  - 
ment  may  be  considered  in  two  stages,  (a)  before  cracks  have 
developed  and  (b)  after  development  of  diagonal  tension 
cracks. 

An  idea  of  the  nature  of  the  web  stresses  may  be 


5 


obtained  by  comparison  with  the  web  stresses  in  a homogeneous 
beam.  In  such  a beam  if  the  tensile  unit  stress  at  a given 
section  is  S and  shearing  unit  stress  is  t,  by  the  ordinary 
formulas  for  combined  stresses,  there  follows 


where  S g is  the  maximum  tensile  stress  on  a section  inclined 
to  the  direction  of  the  tensile  stress  and  t * is  the  maximum 
shearing  stress  on  another  inclined  section.  The  maximum 
inclined  tensile  stress  is  naturally  of  prime  importance } it  is 
found  that  the  angle  of  inclination  is  smallest  near  the 
tension  surface,  so  that  cracks  may  start  nearly  vertically  at 
the  plane  of  the  reinforcement,  then  later  extend  in  the 
diagonal  direction.  It  might  be  noted  that  the  expression  for 
diagonal  tension  also  holds  for  diagonal  compression  if  the 
corresponding  compressive  stress  is  inserted;  the  plane  of  the 
inclined  stress,  however,  is  at  right  angles  to  that  of 
inclined  tension. 


cracks  have  appeared  it  is  obvious  that  no  theory  of  combined 
stresses  can  be  applied.  The  vertical  shear  is  carried  by  the 
unbroken  section  at  the  top  of  the  beam  and  by  the  stiffness 
of  the  horizontal  reinforcing  bars  acting  somewhat  as  dowels. 

If  the  horizontal  bars  are  anchored  by  hooks,  this  portion  of 
the  shear  transferred  by  the  horizontal  rods  may  be  quite  large. 

The  analysis  of  short  deep  beams  is  further  compli- 
cated by  the  fact  that  high  bearing  stresses  are  developed 


In  the  second  stage,  after  a number  of  small  diagonal 


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6 


at  the  supports  and  load  points.  These  high  load  stresses, 
although  perpendicular  to  the  ordinary  compressive  and  tensile 
stresses,  undoubtedly  have  an  effect  upon  the  resistance  of  a 
beam.  Furthermore,  with  the  horizontal  steel  well  anchored, 
it  seems  likely  that  in  the  later  stages  of  loading,  truss  or 
arch  action  is  developed  to  some  extent. 


1 * Fig.  2 

Assume  that  a large  diagonal  tension  crack  appears  near 
the  load  point  as  shown  in  Fig.  1. 

How  the  portion  of  the  beam  to  the  left  of  this 
crack  is  taken  as  a free  body  as  shown  in  figure  2.  It  is 
seen  to  be  subject  to  the  following  forces: the  compression  _c 
in  the  concrete  at  the  top,  the  tension  T in  the  steel  at  the 
bottom  and  perhaps  a very  small  amount  of  tension  Tc,  in  the 
concrete  at  the  end  of  the  crack,  a shearing  stress  S due  to 
load,  partially  carried  by  horizontal  reinforcement,  at  the 
top  vertically  and  reaction  Ss  at  the  bottom  of  the  beam  acting 
as  external  forces.  These  forces  are,  as  shown  in  the 


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7 

Pig.  2 , acting  as  a so-called  arch  action  and  to  hold  the 
equilibrium  condition.  This  free  body  should  act  as  an  arch 
or  as  a curved  column  having  tension  at  the  top  and  compression 
at  the  creek  side,  and  its  resisting  moment  should  be  equal  to 
Ry.  Where  R = Resultant  of  Su  and  C (To  may  be  negli  gible) 
and  some  times  + Sl  . 

y * deflection  of  this  stress  line  from  AB  in  Pig. 2 
If  the  Sc  become slarger , the  y becomes  larger  and  if  the  crack 
opens  nearer  the  support ,y  becomes  larger. 

As  there  is  no  shear  on  the  surface  EP  and  also  no 

the 

tension  there, ^ only  force  acting  to  widen  the  crack  opening 
will  be  that  producing  the  deformation  of  steel  reinforcement  at 
the  bottom,  if  the  effect  of  S or  the  arch  action  is  very  small. 

Then  if  there  is  no  specially  weak  part  in  the  steel 
at  that  point  , new  diagonal  tension  cracks  may  appear  until 
the  St  becomes  large  enough  to  be  taken  into  consideration. 

After  the  arch  action  become  large,  the  opening  of  this 
crack  only  becomes  wider  as  the  load  increases,  while  the  outer 
cracks  will  probably  develop  slowly  due  to  relieving  action 
from  this  crack. 

If  the  shearing  strength  in  the  concrete  at  the  top 
is  strong  enough  to  resist  shearing  failure  under  higher  loads, 
horizontal  tension  cracks  may  be  afterward  observed  between 
concrete  and  steel  starting  from  the  vertical  crack  and  this 
may  cause  the  failure  of  the  beam. 

B.  Action  of  the  Vertical  Stirrups.-  Until  the 
formation  of  diagonal  cracks  the  web  stresses  are  carried 


8 

mainly  by  the  concrete.  But  after  a crack  has  formed,  the 
total  shearing  stress  may  be  carried  by  the  unbroken  area  of 
concrete  and  longitudinal  reinforcement  and  also  by  the  web 
reinforcement  when  there  is  any. 

The  part  of  the  shearing  stress  carried  by  the  longi- 
tudinal steel  contributes  the  greater  part  to  the  cause  of 
diagonal  tension  failures,  as  the  amount  of  shear  which  can  be 
transferred  by  the  steel  is  limited  by  the  vertical  tensile 
stresses  in  the  concrete  in  this  horizontal  section.  These 
shearing  stresses  are  large  because  they  are  concentrated  in  a 
small  sectional  area  of  steel.  Any  shearing  stress  in  excess  of 
the  amount  of  the  vertical  tension  in  the  concrete  in  this 
horizontal  section  must  tend  to  bend  the  longitudinal  steel 
down. 

The  vertical  stirrups  may  be  considered  to  act  in 

two  xmys. 

(1)  To  prevent  the  opening  of  cracks  which  cross  the 
stirrups.  For  this  purpose  bond  stress  is  essential.  Small 
spacing  and  large  number  of  stirrups  has  an  advantage  for 

li.'M  — >>  o 

this  purpose.  However,  on  the  other  side,  if  the„ cracks  do  not 
open,  and  there  is  no  relieving  action,  many  cracks  may  be 
observed. 

(2)  To  transfer  the  shearing  stress  across  the  crack  from 
the  middle  portion  of  the  beam  to  the  end  portion,  the  part  of 
the  shearing  stresses  transferred  by  the  horizontal  reinforce- 
ment is  carried  by  the  action  of  stirrups  to  the  end  portion 
beyond  the  crack. 


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t 

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9 

For  this  purpose,  strength  of  vertical  steel  or 
stirrups  control  the  resisting  strength  of  the  beam. 

The  shearing  stress  distribution  in  a beam  with 
stirrups  may  be  shown  in  Fig. 3. 


Fig.  3. 

C.  Beams  with  bars  bent  up.-  Generally  speaking,  the 
distribution  of  web  stresses  in  beams  with  bars  bent  up  is  very 
complicated  and  indeterminate.  Due  to  distortion  which  takes 
place  in  the  concrete  the  assumption  that  a plane  section  remain 
a plane  section  after  bending  may  not  be  exactly  true,  but  it  is 
used  in  the  following*  analysis. 


Fig.  4 


* 


In  Pig*  4 consider  that  part  of  the  bars  are  hent  up  along  CD  and 
that  the  remainder  run  straight  toward  the  end  B*  At  A these 
bars  have  same  amount  of  tensile  stress*  However,  at  the  point  E 
the  bent  up  bar  carries  lower  stress  than  the  straight  bar  carries 
at  P,  and  the  tensile  stress  caused  by  bending  moment  is  zero  at 
the  point  G* 

The  bent-up  bar  carries  some  amount  of  shearing  stress, 

is 

especially  after  the  crack^developed*  However,  the  bond  stress 
from  C to  G may  be  very  large,  and  also  the  stretching  action  at  C; 
the  bond  stresses  in  this  part  may  be  one  of  the  weak  points  of 
the  beam*  In  the  straight  bars  at  the  bottom,  the  stress  at  P some 
times  may  not  be  much  less  than  at  C,  since  at  B it  is  taking  the 
larger  part  of  the  bending  moment,  and  hence  the  bond  stress 
developed  in  the  portion  CG  will  be  less  than  that  found  in  the 
case  where  all  bars  are  straight,  while  beyond  H and  toward  B 
the  .decrease  in  stress  will  be  rapid  and  the  bond  stress  developed 
will  be  correspondingly  greater. 


' 

* 


. 


] 1 

Fig.  5 shows  the  stress  diagram  in  the  straight  bars  and  bent  up 
bars. 

It  would  seem,  then,  that  the  bending  up  of  the  bars 
tesults  in  greater  vertical  shearing  stresses  between  C and  G,  and 
that  a large  part  of  the  diagonal  tension  developed  here  will  be 
caused  by  the  bent  reinforcement:  and  also  that  in  the  lower  set 
there  is  less  bond  developed  between  C and  H and  hence  the 
diagonal  tension  throughout  this  portion  is  less  than  might  other- 
wise be  expected.  If,  how,  another  bar  be  bent  up,  the  stress 
diagram  is  shown  in  Pig.  6. 


Pig.  6. 

D.  Action  of  Bent-up  Bar.-  The  action  of  a bent-up 
bar  may  also  be  divided  in  two  parts  as  that  of  the  vertical 
stirrups. 

(1)  To  prevent  crack  openings  which  cross  the  bent-up 
bars.  For  this  purpose,  if  the  angle  of  bend  is  proper,  the 
bent  up  bar  may  act  better  than  the  vertical  stirrups. 

(2)  However,  for  transferring  the  shearing  stresses  to  the 
end  portion  from  the  other,  stirrups  have  more  advantages 


« 


f 


13 

As  the  shearing  stress  is  very  small  in  the  flange 
shearing  failure  at  the  flange  may  he  very  rare,  and  in  the 
deep  beaip  with  short  span,  shearing  resistance  in  concrete  is 
very  high.  The  T -shaped  beam  may  oarry  a very  high  load  if 
the  web  reinforcement  used  is  placed  in  the  proper  position. 


c r ' ;l 

■ 

- 


II.  MATERIALS,  TEST  PIECES,  APPARATUS,  AND 
METHODS  OF  TESTING. 


15 


LI.  MATERIALS,  TEST  PIECES,  APPARATUS , AND 
METHODS  OP  TESTI1TG 

5.  Materiel s.  - The  materials  used  in  making  the  test 
beams  were  similar  in  character  to  those  used  for  several  years 
past  at  the  Uniy  ersity  of  Illinois  in  making  reinforced  concrete 
test  specimens,  and  they  may  be  considered  to  be  represents ive 
of  the  best  1a  terials  used  for  this  class  ofw«rk  in  this  section 
of  the  country. 

The  cement  wa.s  furnished  by  the  Universal  Portland  Cement 
Company.  The  mild  steel  rods  used  for  web  reinforcement  ?®re 
furnished  by  the  Illinois  Steel  Company.  The.  corrugated  bars 
used  for  longitudinal  reinforcement  were  supplied  by  the  Corru-  » 
gated  Bar  Company. 

Steel.  - Por  horizontal  reinforcement  1 l/4in.round  high- 
carbon  corrugated  steel  bans  were  used,  and  for  vertical  strings 
3/8,  1/2,  and  5/8  in.  round  mild  steel  bars  were  used.  Coupons* 
for  tension  tests  were  cut  from  the  ends  of  bans  used  in  the 
beams.  The  results  of  the  test  were  quite  uniform.  Ta/ble  / 
shows  the  average  data  of  the  tests. 


< 


; ; 


- 

. 

. . 


. 


TABLE  1 


16 


w 


\ 


TENSION  TESTS  OE  STEEL 


No.  Diameter  Kind  Unit  stress  Ultimate  Percent  Percent 


of  Bar  of  steel  at  yield 

point 
lbs.  per 


sq.  m 

1 

3/8 

Mild 

42,380 

2 

1/2 

40,120 

3 

5/8 

» 

39,610 

4 

i i/f 

High  Car- 
bon Corr. 

52,400 

strength  elongation  reduction 


IBs.  per 
sq.  in. 

in 

8 in. 

of  ar 

57,330 

30.2 

67.3 

57,700 

29.2 

67.8 

61,270 

28.3 

63.9 

88,570 

21.3 

26.7 

Cement.  - Universal  portland  cement  was  used.  This  cement 
was  new,  having  Been  received  from  the  factory  in  December ,1921. 
It  passed  satisfactorily  the  tests  required  By  the  standard 
specifications  for  cement  of  the  American  Society  for  Testing 
Materials.  The  water  required  for  -plasticity  By  the  Vicat  test 
was  found  to  Be  24.5  percent  By  weight.  The  specific  gravity 
By  the  Le  Chatelier  flash  test  was  3.12.  Tests  of  tensile  and 
compressive  strength  are  given  in  Table  3,  wherein  the  values 
represent  the  average  of  tension  tests  on  six  Briquettes  and 
compression  tests  on  five  2 x 4 -in.  cylinders.  The  mo r tan  mix- 
tures are  123  By  weight. 


Table  2 

TESTS  OE  CEMENT  AND  MORTAR 


Material 

Tensile  strength 
IB.  Tier  sq.  in. 

Compressive  strength 
IB.  per  sq.  in. 

7 days 

28  days 

28  days 

i 

Neat  Cement 

— 697 

8345 

1:3  Ottawa,  sand 

mortar  214 

311 

3320 

— • 3 At  tic  a sand 

mortar  309 

488 

4220 

n 


Fine  aggregate.  - The  sand  used  wasNgood  quality,  clean, 
hard  and  well  graded,  obtained  from  near  Attica,  Indiana.  It 
weighed  112  lbs.  per  cu.  ft.  compacted  in  the  standard  way,  and 
its  specific  gravity  was  2.67.  The  voids  in  the  dry  sand  we re 
33.2  percent.  Table  3 gives  the  results  of  mechanical  anaJLysis 
of  this  sand,  from  which  the  fineness  modulus  is  found  to  be 
3.35  and  the  surface  modulus,  16.6. 


TABLE  3 

MECHANICAL  ANALYSIS  OE  SAND 
( Tyler  Standard  Sieves) 


Sieve 

No. 

Percent 

passing 

3/8 

100 

4 

97 

8 

78 

14 

51 

28 

25 

48 

10 

100 

4 

For  use  in  designing  the  concrete  mixture,  mortar -voids 
tests  were  made  using  this  sand.  Curves  showing  the  vaAue  of 
the  voids  in  the  mortar,  Vm,  and  the  water  content  of  the  mor- 
tar, Wm,  for  different  mixes  and  water  contents  are  given  on 
the  following  page.  The  volume  of  water  per  unit  volume  of  mor- 
tar that  produces  the  maximum  density  is  used  as  a standard  for 
reference  and  is  termed  the  "Basic"  water  content. 


< « 

, 

• 

i 

i ' ; :> 

\la 

-b  V* 
5 * 


£ 

( 

•5 

& 

5; 


•JQ 

s 


o.s  o 


o.4c 


a 3o 


0.2o 


Charactamsh'c  McAor  Voids  Curve.* 
for  rfttica  Sand 


|.  lr>  GdSlc 
|,4-  T3«s>'c 
1.2-  (basic 
).0  (3asit 


<5?/  _ Absalo4iZ  Wn/umr? — of  SanJ  T 
SC  j4bz>°  / utzvo  I u m a erf  Camanr 


C 

\ 3 s 

*2.0 

10 

20 

OJO 

Vo 

wafer  per 

0.3  0 


04-0 


o.so 


pT 


-\«x  ■«  &;nuUV|  SVj\  <U"~A 


046 


<&li 


or?:, 


a 

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i 

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3- 


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Sc  S 


O-KCi 


3 « ,Q 


0£0 


0\;j 


,j  O'iA 


.wVi  ->v>Ytarc\  \o  Xo'-j  -V\vv\i  >&c\  -vvWj  'oV 


la 


Coarse  Aggregate.  - The  coarse  aggregate  used  was  a good 
quality  of  screened  gravel  from  near  Attica,  Indiana,  of  sizes 
varying  from  11/4  in.  to  1/4  in.,  according  to  the  sieve  analy- 
sis of  Table  4.  The  pebbles  were  rounded  and  somewhat  irregu- 
lar and  mainly  of  calcareous  material.  The  specific  gravity 
was  2.69  and  the  weight  per  cubic  foot  under  standard  methods 
of  compacting  was  101  pounds;  the  voids  in  the  gravel  are  hence 
found  to  be  40.0  percent. 

TABLE  4 

MECHANICAL  ANALYSIS  OF  GRAVEL 
(Tyler  Standard  Sieves) 

Sieve  Percent 

No.  passing 


1 1/2  in. 

100 

1 1/4  H 

98 

1 « 

89 

3/4  M 

59 

1/2  " 

35 

3/8  " 

13 

No . 4 

3 

Concrete.  - The  concrete  was  1:2:4  mixture  by  loose  vol- 
ume and  the  proportions  by  weight  were  also  determined.  V/ith 
these  proportions  the  ratio  of  absolute  volumes  of  send  and  ce- 
ment was  2,75.  Basic  water  content  was  determined  by  means  of 
themo.rtar-vo ids  test  on  the  sand  and  cement  end  1.2  times  basic 
water  conoenc  was  used  throughout  all  specimens. 


19 


In  making  the  beams  the  workability  of  each  batch  of  con- 
crete was  measured,  by  means  of  the  slump  and  flow  table  test. 

In  the  slump  test  the  settlene  nt  or  slump,  of  a truncated  cone 
of  fresh  concrete  was  measured  when  the  mold  was  removed.  The 
cone  was  12  in.  high,  and  the  bases  were  4 and  8 in.  'in  diam- 
eter. In  the  flow  test  a,  truncated  cone  about  6 inches  high 
and  having  bases  6 and  11  in.  in  diameter  was  placed  on  a table, 
the  mold  was  removed,  and  the  table  was  raised  and  dropped  thru 
a distance  of  1/2  inch  fifteen  times.  The  flow  is  measured as°^ 
the  final  diameter  to  the  original  diameter  of  the  bottom  of 
the  cone.  Care  was  taken  in  measuring,  mixing  and  tamping  to 
secure  as  uniform  a concrete  as  possible.  Men  accustomed  to 
nixing  concrete  and  making  test  beams  were  employed  in  the  work. 
The  mixing  was  done  with  a Wonder  batch  mixer,  of  which  the 
capacity  is  about  6 cu.  ft.  The  rectangular  beams  required  4 
batches  and  the  £ -beams  required  5 batches. 

For  the  first  batch  in  each  beam,  gravel  pe„ssing  all/2  in. 
screen  Y/as  used  in  order  to  allow  the  concrete  to  flow  easily 
around  the  reinforcing  bars. 

In  mixing  the  concrete,  the  mixer  was  first  washed  out, 
then  sand,  gravel  and  cement  were  introduced  in  order  named, 
and  the  mixing  water  was  added  last.  The  batch  was  then  mixed 
for  four  minutes,  dumped  into  a tight  metal  pan,  and  shoveled 
into  the  form.  Control  cylinders  were  made  with  each  batch; 
most  of  these  were  tested  with  the  beams  but  a few  were  tested  at 
7 and  28  days.  The  average  strength  at  7 days  was  1950  lb. per 
sc:,  in.;  at  28  days,  3230  lb.  per  sq.  in.  The  average  strength 


20 


of  cylinders  tested  at  the  age  of  the  "beams  with  which  they 
were  made  is  given  in  Table  5 together  with  the  data  on  slump, 
flow,  and  density  of  the  freshly  mixed  concrete. 

TABLE  5 

PHYSICAL  PROPERTIES  OP  CONCRETE 


(Each  value 

represents 

ave.  of  4 

or  5 6 

x 12  in. 

cylinders) 

Corres . 

Beam  Ho. 

Age  at 
Test 
Bays 

Compressive  Mod. of 
Strength  Elasti- 

Ib.per  sq.in.  city 

Slump 

in. 

Plow  Density 

Percent  of  of 

Orig.Dian.  Concrete 

221-1 

61 

4076 

4,165,000 

0.4 

149 

s'. 

221-2 

61 

3696 

3,575,000 

0.5 

164 

.882 

222-1 

60 

4522 

4,030,000 

0.9 

151 

/ 

.099 

222-2 

59 

4337 

5,360  ,000 

0.4 

155 

.806 

/ 

.390 

223-1 

60 

4124 

4,355,000 

0.7 

156 

223-2 

61 

3689 

4,440,000 

0.6 

158 

.806 

) 

.877 

i 

224-1 

62 

■4106 

4,131,000 

0.8 

149 

224-2 

61 

3790 

4,130,000 

0.4 

157 

,88p 

225-1 

62 

3788 

3,990,000 

1.0 

147 

.8^2 

225-2 

61 

4041 

4,375,000 

1.4 

159 

.882 

1 

226-1 

62 

4037 

3,920,000 

1.1 

152 

.809 

{ 

226-2 

60 

4331 

4,916,000 

0.3 

145 

.8^ 

/ 

.800 

227-1 

62 

3799 

3,894,000 

1.4 

158 

227-2 

60 

4346 

4,272,000 

0.5 

159 

.802 

f 

228-1 

62 

4058 

4,540,000 

1.0 

150 

.887 

228-2 

60 

4152 

4,788,000 

0.8 

168 

{ 

.882 

229-1 

62 

3931 

4,315,000 

1.9 

163 

.882 

229-2 

60 

4203 

4,675,000 

0.4 

153 

i 

.882 

Average  4057 

4,326,000 

0.85 

155 

- — — — — i — 

.883 

, . >,  .-'v’  , ; 


t 


c > < 


t • t 


'9. 


t * 


c c 


6.  Test  Beams.  - Two  beams  of  each  of  the  nine  types,  a to- 
tal of  eighteen,  were  made.  Three  types  were  jt  -shaped,  and 
the  rest  were  rectangular  beams.  The  latter  have  a cross  sec- 
tion of  8 x 24  in. , and  the  former  were  of  such  a cross  section 
that  the  flange  width  was  20  in. , flange  depth,  6 in. , web 
width,  8 in. , and  total  depth,  24  in.  The  centroid  of  the  lon- 
gitudinal reinforcement,  which  was  placed  in  two  layers,  was  21 
in.  below  the  top  surface,  and  extended  the  full  length  of  all 
beams  except  in  No.  229-1  and  2,  which  had  two  bent  up  bars  in 
the  outer  third  of  the  span  length.  The  percentage  of  longitu- 
dinal. steel  in  all  beams  was  2.33  percent. 

All  horizontal  reinforcing  ba.rs  had  hooks  of  3 1/2  in.  ra- 
dius at  both  ends  except  No.  221-1  and  2,  which  had  straight 
horizontal  bars  without  hooks. 

In  beams  No.  229-1  end  2,  having  bars  bent  up,  the  first 
bend  began  at  a point  6 in.  outside  the  load  point  and  passed 
diagonally  upward  at  about  45  degrees  with  the  horizontal,  axis. 

A second  ba.r  was  bent  up  parallel  to  the  first  and  so  hooked 
that  the  highest  part  of  the  hook  came  about  2 inches  below  the 
top  surfa.ce,  and  2 ig.  from  the  end  of  the  beam.  The  general, 
arrangement  of  reinforcement  and  other  details  of  these  beams 
are  shown  in  Figure  15  In  the  beams  with  stirrups,  the  latter 
passed  under  the  longitudinal,  bars  and  extended  to  within  1 in. 
of  the  top  surface.  Two  u stirrups  T;ere  used  to  form  the  equiv- 
alent of  a W- shaped  stirrup  in  all  cases.  The  upper  ends  of  all 
stirrups  had  hooks  of  about  1 1/2  in.  radius.  Table  6 gives  the 
details  of  the  stirrups  used. 


22 


TABLE  6 


SPACING  AND  SIZE  OE  VERTICAL  STIRRUPS 


Beam  No 


Stirrups 

Type  Spacing-in.  Liameter-in 


228-1  & 2 


22 4-1  & 2 


225-1  & 2 


223-1  & 2 Rectangular 


227-1  & 2 


226-1  & 2 Tee-Section 


ii 


11 


11 


4 


4 


7 


7 


3/8 

1/2 

5/8 

3/8 

1/2 

5/8 


7.  Making  of  the  Beams.  - The  beams  were  made  in  built-up 
wooden  forms'  on  the  floor  of  the  Concrete  Laboratory,  being  pre- 
vented from  adhering  to  the  floor  by  a strip  of  building  paper. 
The  forms  are  shown  by  the  photographs  on  following  pages.  In 
placing  the  steel  in  the  forms,  care  was  taken  to  locate  it  as 
nearly  as  possible  in  the  position  shown  on  the  details. 

The  longitudinal  steel  was  supported  by  1/4  in.  bars  at  the 
proper  distance  above  the  bottom  of  the  beam,  while  the  stirrups 
were  wired  at  the  bottom  to  the  longitudinal  reinforcement,  and 
at  the  top  to  a 1/4  in.  horizontal  spacing  bar.  This  wiring  and 
bracing  kept  the  stirrups  in  position  during  the  pouring  of  the 
concrete.  Corks  about  11/4  in.  in  diameter  and  from  5/8-  to  3/8 
in.  in  height  for  the  different  diameters  of  stirrups  were  lacked 
to  the  form  in  all  places  where  gage  points  were  to  be  located 
and  served  not  only  to  save  much  chipping  in  exposing  the  steel 

lines,  out  also  helped  to  keep  stirrups  in  their  nrouer 
position  during  pourin.<  . 


rectangular  be  ans 


26 


After  the  steel  and  corlcs  had  been  placed,  the  concrete  was 
poured.  In  depositing  the  concrete,  care  was  taken  to  get  it 
around  all  of  the  steel,  and  it  wa s well  puddled  to  prevent  the 
formation  of  pockets  of  any  kind.  In  addition  to  the  tamping, 
the  sides  of  the  form  were  rapped  with  mallets  to  aid  in  compact- 
ing the  material  and  to  improve  the  appearance  of  the  surface. 

8.  Storage  of  Specimens.  - The  forms  were  removed  in  five  to 
seven  days  after  the  beams  were  made,  and  the  beams  were  stored 
in  the  laboratory  and  covered  with  burlap  which  was  made  wet  from 
time  to  time. 

The  temperature  of  the  room  in  which  the  beams  were  cast 
and  stored  ranged  from  68  to  80  degrees  Fahrenheit.  The  cylin- 
ders were  stored  in  the  damp  a,ir  of  the  moist  room  at  a temper- 
ature of  about  70  degrees  F. , and  were  removed  to  the  testing 
laboratory  one  day  before  testing. 

9.  Method  of  Testing.  - The  tests  were  made  in  the  300,000 
lbs.  Olsen  testing  machine.  The  span  length  Y/as  9 ft.  The 
beam  was  supported  at  the  ends  by  rocker  bearings  which  in  turn 
rested  on  the  table  of  the  machine,  as  shoYrn  by  the  photograph 
on  the  following  page. 

The  top of  the  rocker  carried  a cylindrical  steel  bearing  of 
3/4  in.  radius,  while  the  bases  were  slightly  curved  to  allow 
a rocking  action  with  changes  in  the  length  of  the  lov/er  surface 
of  the  beam.  The  beam  was  loaded  at  the  one-third  points  of  the 
span,  the  load  being  transferred  from  the  machine  through  a 
spherical  hearing  block,  24-in.  I-beam,  and  two  cylindrical  rol- 
lers. Iron  bearing  plates  1 x 5 x 8.5  in.  were  placed  between 


27 


the  beam  and  the  roclcer  supports.  A layer  of  plaster  of  paris 
v/ as  placed  between  these  bearing  plates,  and  the  beam  to  overcome 
uneveness  of  surface  and  was  allowed  to  set  under  such  load  a,s 
came  from  the  weight  of  the  beam  and  the  apparatus  used  in  load- 
ing. A load  of  5000  lbs.  was  used  as  an  initial  load  in  order 
to  tighten  up  all  the  loading  apparatus  before  starting  the  test. 
Deflection  was  observed  at  the  middle  of  the  span  by  means  of  a 
fine  copper  wire  suspended  at  constant  tension  between  points 
over  the  supports  and  at  the  middle  of  the  depth  of  the  beam. 

The  wire  passed  in  front  of  a paper  scale  attached  to  the 
side  of  the  beam  at  midspan.  The  scale  was  pasted  on  the  face 
of  a minor  and  readings  were  obtained  by  lining  up  the  thread 
and  its  reflection.  These  readings  were  accurate  to  0.01  in. 

To  obtain  the  longitudinal  elongation  and  shortening  at 
the  top  and  bottom  of  the  beam,  the  strain  gage  v/a,s  used.  Dour 
strain  gages  were  used  for  this  test;  namely,  No.  1,  No.  2040, 

No.  1603,  and  No.  1604.  These  are  all  of  the  Derry  type  of 
strain  gage,  concerning  which  informalion  is  given  in  Table  7. 


TABLE  7 

STPAIN  GAGE  CONSTANTS 


Gage 

i No. 

Gage  Length 

Hul tiplication  Satio 
From  Used  for 

Calibration  Calculation 

Material  of 
Instrument 

No. 

1 

8” 

7.587 

7.5 

Steel 

No. 

2040 

8"  and  4” 

5.089 

5.0 

"Invar”  steel 

No. 

1603 

4« 

7.473 

7.5 

Aluminum 

No. 

1604 

4» 

75.36 

7.5 

n 

lhe  photograph  on  a following  page  shows  the  strain  gages  and 
their  applicalion. 


30 


For  a more  general  description  of  this  type  of  extensometer 
and  its  use,  reference  is  made  to  a paper  by  Willis  A Skater  end 
Herbert  F.  Moon,  in  the  "American  Society  for  Testing  Materials" 
1913,  on  "The  Use  of  the  Strain  Gage  in  the  Testing  of  Materials"* 
and  to  Bulletin  Ho.  64,  University  of  Illinois.  The  method  out- 
lined in  these  papers  was  followed  in  these  tests. 

Crack  openings  we re  measured  with  a fair  degree  of  accuracy 
by  comparison  with  the  opening  of  a screw  micrometer. 

In  the  test  of  the  first  beam,  it  was  found  that  the  ribst 
important  feature  of  preparing  a beam  for  strain  gage  tests  lies 
in  the  preparation  of  gage  holes. 

If  the  holes  we re  good,  the  readings  could  be  taken  quickly 
and  accurately.  However  it  was  impossible  to  obtain  reliable 
readings  from  shallow  or  irregular  holes.  The  gage  line  is  a 
gaged  length  between  a pair  of  gage  holes  and  is  the  length  over 
which  the  deformation  is  measured.  The  gage  holes  were  small 
holes  about  0.05  inch  in  diameter,  drilled  in  the  steel  reinforce- 
ment and  in  steel  plugs  which  were  imbedded  in  the  concrete  at 
the  top  surface  of  the  beam. 

In  order  to  expose  the  steel  so  that  ga,ge  holes  might  be 
drilled,  corks  were  attached  to  the  forms  in  the  proper  places 
before  pouring  the  concrete.  After  the  drilling  of  the  gage 
holes,  the  specimens  were  white-washed  before  being  placed  in 
the  testing  machine  in  order  that  the  cracks  might  be  easier  to 
find  and  mark.  Loe,ds  were  applied  at  a slow  speed  of  the  machine 

the  rate  of  speed  being  .05  in.  per  min.  with  the  machine  mnning 
idl  e . 


g Str  -in  gages 


Application  of  strain  g~ge 
in  testing 


oo 


Cracks  were  noted  and  marked  at  loads  of  15,000,  25,000, 

35.000,  50,000,  60,000,  70,000,  80,000,  90,000,  105,000  and 
120,000  11).  and  at  additional  increments  of  10,000  lb.  Strain 
measurements  were  taken  at  loads  of  35,000,  70,000,  105,000, 

150.000,  and  200,000  lbs.  and  in  the  case  of  higher  loads,  fur- 
ther readings  were  taken  at  the  maximum  load. 

At  the  initial  loading  two  sets  of  zero  readings  were  taken 
for  all  gage  lines  and  the  average  of  these  was  used  as  the  zero 
readings. 

In  the  numbering  of  gage  lines,  a.  uniform  system  v/as  udgd. 
Beginning  at  the  south  end  on  the  west  side  an  the  beam  was  set 
in  the  machine,  gage  lines  on  the  first  stirrup  were  numbered 
from  1 to  5,  on  the  second  from  11  to  15,  etc.,  starting  from 
the  top.  Similarly,  slanting  on  the  ea.st  side  at  the  south  end, 
the  gage  lines  on  the  first  sturrup  were  numbered  from  6 to  10, 
on  the  second,  from  16  to  20,  etc. 

On  the  longitudinal  bars  all  gage  lines  v/ere  numbered  from 
101  on  the  west  side  and  from  201  on  the  east  side,  numbering 
from  the  south  end  northward;  on  the  compression  fa.ce  the  gage 
lines  were  numbered  beginning  with  300  at  the  south  end. 

In  a few  of  the  tee -beams,  additional  gage  lines  on  the  com- 
pression face  were  numbered  beginning  with  wi  on  the  west  side  of 
-me  center  line,  and  El  on  the  ea,st  side;  also  a.  few  lines  set  on 

the  sides  of  the  tie-flange  were  numbered  A1  on  the  west  side, 
and  B1  on  the  east  side. 


34 


III.  EXPERIMENTAL  DATA  ALTD  DISCUSSION 

1 0 . De scrmtion  of  Figures t Photographs  raid  Tables 

Eor  use  in  the  explanation  of  analysis  or  stress  distribution 
figures  have  been  made  and  inserted  in  a convenient  place  to  use. 

Typical  figures  showing  all  detalLs  required  for  the  construc- 
tion of  the  beams  are  inserted  on  pages  > 7 to  231. 

Seven  photographs  were  taken  to  show  clearly  about  the  equip- 
ment used  and  are  inserted  in  suitable  planes. 

The  five  photographs  shown  on  pages  __  71  tO  63  were  taken 

to  show  the  typical  failures. 

Thirty- six  photographs  on  pages  84  fto  101 were  taken  on 

each  side  of  each  beam  to  show  the  location  of  creeks  and  also 
the  loads  as  the  creeks  progressed.  The  figure  on  the  cracks  de- 
note the  load  in  units  of  1000  lbs. 

Dia.gram  No.  1 shows  the  characteristic  mortar  void  curves 
for  the  seed  used  in  the  beams. 

Diagram  No.  2 shows  the  observed  relation  between  distance 
from  load  point  and  angle  of  inclination  of  cracks. 

Diagrams  on  pages  to  t22  show  the  relation  between  the 
unit  stress  in  the  stirrups  and  the  applied  load  for  each  gage 

line. 

Diagrams  on  pages  n_8  to  226.  show  the  relation  between 
crack  opening  and  stress  carried  by  web  reinforcement  and  hori- 
zontal bars. 

Beam  deflection  diagrams  are  shown  on  pages  to  no 

- ■ ■ ■ ■■■  ■ L- ■ " - 1 *""  — 


. 


< • - 


X •.  :■ 


r~ 


•* 


* ..  ... 

: . 


* 


*■ 


i n 

, 


Tables  were  ms.de  and  inserted  in  suitable  places  when  it 
was  thought  that  they  would  add  to  the  clearness  of  the  work. 

11.  Deflections  of  Berms . - The  lpad- deflection  diagrams 
show  the  deflection  of  the  beams  at  loads  at  which  the  stress 
measurements  were  made.  It  appears  that  while  diagonal  tension 
cracks  were  developing  the  rigidity  of  the  outer  thirds  of  the 
beams  decreased  somewhat  making  the  deflection  of  the  outer 
thirds  comparatively  large  a,s  compared  to  the  deflection  at  mid- 
span. However,  at  loads  near  tensile  failure  at  midspan,  the 
shape  of  the  deflection  curve  changed  again  and  the  deflection 
at  the  center  increased  more  rapidly.  The  difference  in  the 
rate  of  deflection  is  apparent  in  the  load-deflection  diagrams. 

The  usual  calculation  of  deflection  in  reinforced  concrete 
beams  are  based  upon  the  following  assumptions: 

1.  The  representative  or  mean  section  ha,s  a depth  equal  to 
the  distance  from  the  top  of  the  beam  to  the  center  of  the  steel. 

3.  Tlie  material  sustains  tension  as  well  as  compression) 
both  following  the  linear  law. 

3.  The  proper  mean  modulus  of  elasticity  of  concrete 
equals  the  average  or  secant  modulus  computed  at  the  working 
compressive  stress. 

4.  The  allowance  for  steel  in  computing  the  moment  of 
inertia,  of  the  mean  section  should  be  based  on  the  amount  of 
steel  in  the  mid-section. 

The  effect  of  cracks  is  partly  covered  by  neglecting  the 
concrete  belo w the  horizontal  reinforcement.  However,  in  deep 
beams  with  small  spans,  the  effect  of  diagonal  shearing  cracks 


. 

r 

, 

36 


and  deflection  due  to  direct  shearing  stress  may  need  to  he  taken 
into  consideration  in  computing  the  total  deflection. 

In  this  thesis,  the  limited  time  does  not  allow  further  stu- 
dy of  the  relations  between  the  deflections  and  the  other  elastic 
properties  of  the  beams. 

A.  Beams  Without  Web  Reinforcement 

12.  Motes  of  Test.  - The  location  of  cracks  are  all  referred 
to  the  load  points  and  supports.  The  abbreviation  for  north-west 
load  point  is  M.W.L. , and  of  south-east  support  is  S.E.S.,  etc. 

Most  of  the  cracks  apparently  extended  through  the  thickness 
of  the  bean,  but  in  these  notes  the  cracks  on  each  side  were 
treated  as  if  they  were  separate  ones. 

a.  Beams  without  Hooks. 

Beam  Mo.  221-1:  Two  cracks  appeared  at  the  load  of  25,000 

lbs.  10  in.  from  S.W.L.  and  in  mid-span  in  W.  side.  At  the  load 
of  50,000  lbs,  several  cracks  appeared  in  both  West  and  East 
sides,  some  of  them  reading  about  11  in.  from  the  bottom.  The 
first  diagonal  crank  appeared  at  Morth  side  10”  Morth  from  M.W.L. 
at  the  load  of  55,000  lbs.,  stenting  from  near  the  horizontal 
bar  and  making  an  angle  of  nearly  45  degrees  with  the  horizontal, 
until  the  middle  depth  of  web  was  reached;  with  increasing  loads 
this  cra,ck  developed  both  upward  and  downward. 

At  the  load  of  75,000  lbs.  diagonal  tension  crack  appeared 
a.t  both  sides  at  both  ends  and  the  diagonal  tension  crack  in 
1:*  '■  * side  °Pened  so  tilat  if  the  horizontal  bars  had  no  cor- 

rugations the  beam  might  have  failed  at  a lower  load.  At  the 

lrjr  of  90 »000  lbs*  c racks  reached  about  4”  below  the  load  point 


37 


and  shear  failure  approached.  At  the  load  12,000  lbs.  diagonal 
tension  crack  opening  observed  as  follows:  IT. 7/.  .05";  17. E.  .04"; 

S,T.Y.  .02";  S.E.  .02".  The  failure  came  suddenly  at  the  load 
154,100  lbs.  by  slipping  of  bare  ombined  with  shearing  failure 
atthe  top  of  the  beam  near  the  load  point. 

Beam  l!o.  221-2:  Cracks  did  not  appear  until  at  the  load 

50.000  lbs.  where  a crack  under  the  S .71. L.  went  up  about  12  in. 

A diagonal  tension  crack  was  found  at  the  load  60,000  lbs,  v/ent 
up  about  14"  high  starting  from  14  in.  South  from  the  S.E.S.  to- 
ward the  S.E.L.  At  the  load  70,000  lbs.  a diagonal  tension 
crack  appealed  in  S.  W.  side  and  developed  quickly.  At  the  load. 

13.000  lbs.  and  14,000  lbs.  horizontal  cracks  eh  the  ends  of  the 
beam  from  10 "to  8"  high  from  the  bottom  appealed,  showing  some 
tensile  stress  in  this  part.  At  150,000  lbs.  when  the  testing 
machine  was  stopped  to  start  measuring  strains  at  this  load,  the 
beam  failed  suddenly  by  the  vertical  tension  failure  at  the  ITorth 
end  together  with  shear  failure  at  the  top.  The  vertical  tension 
failure  followed  very  suddenly  from  this  point  to  the  other  end 
of  the  beam. 

b.  Beams  with  Hooks. 

Beam  Bo.  222-1:  On  each  side  of  the  beam  two  large  holes 

under  the  reinforcement  v/ere  visible.  The  first  crack  appeared 
ah  25,000  lbs.  at  6"  from  S.E.L.  under  the  horizontal  reinforce- 
ment, and  at  30,000  lbs.  two  cracks  were  found;  at  6"  and  14" 
north  from  the  S.E.L.  and  6"  south  from  S.W.L.At  the  load  45,000 
l^.j.  many  small  cracks  appeared  all  over  the  middle  third  adid 


some  of  them  were  found  a few  inches  outside  of  it.  At  the  load 


38 


65.000  lbs.  first  diagonal  tension  crack  was  observed  at  14”  north 
from  S.V/.L.  and  at  the  load  70,000  lbs.  this  crack  lengthened 
about  24”  to  a point  about  8”  under  the  top  surface.  At  the 
load  80,000  lbs.  a big  diagonal  tension  crack  was  observed  at  the 
northeast  side  and  developed  rapidly.  The  diagonal  tension 
crank  in  the  south  side  reached  a point  5”  under  the  S.E.L. 

Crack  openings  were  almost  same  width  on  both  sides; at  the  load 

• * 

105.000  lbs.  they  were  about  .025”  and  at  the  load  135,  ;00  lbs. 
.05”,  and  at  the  load  151,000  lbs.,  .07”.  Shearing  stress  in  the 
concrete  at  the  top  of  the  beam  near  the  IT. L.  caused  the  failure. 
It  should  be  noticed  that  horizontal  cracks  appeared  on  the  N.E. 
side  at  the  loa,d  of  110,000  lbs.  and  also  alter  failure  tension 
crack  appeared  in  the  top  of  the  beam  9”  north  from  the  N.W.L. 

at  the  top  of  the  beam.  Ultimate  load  was  167,500  lbs. 

Beam  Ho.  222-2:  N o cracks  appeared  at  the  load  25,000, 

35,000,  40,000  lbs.  First  cracks  appeared  at  the  load  50,000 
lbs.  6”  north  from  S.W.L. , 6” high;  14”  north  from  S.W.L. , 10.5” 
high;  14”  south  from  N.W.L. , 1”  high;  10”  north  from  H.W.L. , 

1”  high;  2”  south  from  S.E.L. ,10”  high;  1”  south  from  center  in 
E.  side,  10”  high;  2”  south  from  1T.E.L.  , 10”  high;  6”  south  from 
U.E.L. , 6”  high.  At  the  load  70,000  lbs.  first  diagonal  cracks 
were  observed  at  both  ends  except  N.W.  side.  At  the  load  76,000 
lbs.  big  diagonal  tension  cracks  suddenly  appeared  at  the  sixth 
end  and  beam  of  the  testing  machine  dropped  for  a while.  At  the 
load  120,000  lbs.  this  crack  opened  0.675"  on  the  S.E.  side. 
Failure  oceured  at  the  load  128,000  lbs.,  caused  by  vertical 

shear  at  the  south  side  load  point,  load  dropped  off  to  125,000 

lbs. 


I' 


", 


< 


1 * 


39 


13.  Be iams  Without  Y/eb  Reinforcement 

The  dangerous  diagonal  tension  cracks  usually  appeared 
about  at  the  middle  point  of  the  outer  third  of  the  span  start- 
ing from  the  reinforcement  at  the  load  from  55,000  to  70,000  lbs. 
It  should  be  borne  in  mind  that  the  horizontal  reinforcement  was 
not  plain  rods  but  high  carbon  corrugated  steel  bans.  On  the 
appearance  of  these  cracks,  their  direction  curved  bending  toward 
the  load  point.  As  the  load  on  the  machine  was  increased,  the 
cracks  lengthened  and  extended  upward  to  within  a few  inches  un- 
der the  load  point,  and  the  upward  extension  of  this  crank  almost 
stopped,  while  new,  large  diagonal  tension  cracks  appeared  neaner 
the  support,  suddenly  connecting  these  former  cracks  in  nearly  a 
straight  line,  and  in  some  cases  the  load  dropped  for  a while. 

After  these  cracks  were  connected,  the  diagonal  tension 
cranks  opened  widely,  causing  the  bond  resistance  between  con- 
crete and  steel  reinforcement  to  fail  suddenly. 

If  the  plain  rods  had  been  used  instead  of  corrugatedbar  as 
in  the  longitudinal  reinforcemen  t failure  might  have  come  at  low- 
er loads.  Maximum  crack  opening  for  these  final  diagonal  tension 
cracks  were  observed  to  be  about  0.1  in.  wide. 

Shearing  stress  carried  by  the  horizontal  bars  near  the 
cranks,  acted  as  a tearing  stress  or  a vertical  tensile  stress 
of  which  the  intensity  is  a.  maximum  at  the  crack  and  decreased 
toward  the  end,  between  concrete  and  reinforcement,  end  whenever 
tensile  strength  in  the  concrete  between  horizontal  reinforcing 
oa.rs  and  also  oe  u,reen  horizontal  reinforcing  bans  and  outer  sur- 
face oi  the  web  of  the  beam,  reaches  the  ultimate  strength,  the 
beam  may  fail  by  slipping  of  the  horizontal  reinforcement. 


} . 


>■ 


< ' 


I 


i 

. 

■ 


40 

On  the  other  hand  concrete  at  the  top  of  the  beam  carrying 
shearing  stress,  lost  much  area  as  the  diagonal  tension  crack 
extended  toward  the  load  point.  If  the  shearing  resistance  in 
concrete  reached  the  ultimate,  failure  of  the  "beam  may  he  caused 
hy  this  shear  failure. 

Failure  of  the  beans  with  straight  bars  cane  suddenly  with 
shear  failure  at  the  top  and  the  failure  caused  by  slipping  of 
bars  at  the  bottom  at  the  sane  time  in  both  causes;  it  is  inpos- 
sible to  find  which  failure  occurred  first,  and  thus  to  distin- 
guishthe  critical  source  of  the  failure. 

In  the  beans  vhich  lave  hooks  on  the  horizontal  bars,  slip- 
ping of  the  bars  may  be  prevented  by  the  hooks  to  some  extent, 
and  failure  of  this  kind  of  beans  are  caused  by  shearing  stress 
in  the  concrete  at  the  top  followed  by  large  cracks  appearing 
at  the  ends  around  the  hooks. 

The  beans  without  web  reinforcement  carried  an  average 
load  of  157,000.  The  average  unit  shear  was  525  lbs.  per  sq.  in. 
This  means  0.121  of  the  average  ultimate  compressive  strength 
of  the  concrete. 

1 4 . Effect  of  Hooks  at  the  Ends  of  Beans . 

Effect  of  hooks  on  the  horizontal  bars  prevent  slipping 
of  reinforcement  in  the  concrete,  consequently  crack  opening 
may  be  prevented  to  some  extent.  It  may  be  the  reason  that  the 
final  large  cracks  started  from  the  points  nearer  the  support 
in  the  beans  with  hooked  bars  than  the  one  in  the  beans  with 


straight  bars. 

However,  they  did  not  show  any  effect 
shearing  resistance  in  the  concrete  at  the 


materially  on  the 
o0P  of  the  beans . 


41 


Beams  with  hooks  at  the  ends  of  the  reinforcement  all  failed 
hy  shearing  failures  at  the  top  of  the  beam,  and  did  not  fail  by 
vertical  tensile  failure  at  the  bottom  of  the  beam.  Therefore 
in  the  deep  beams  for  a short  span  with  web  reinforcement,  it  may 
also  be  necessary  to  have  hoolcs  at  the  ends  of  the  reinforcement 
even  when  corrugated  bars  are  used. 

1 5 . Position  of  the  Feutral  Axis 

In  the  beam  under  flexure,  the  location  of  the  neutral  axis 
depends  upon  the  s txeng^h  of  concrete  and  reinforcing  steel,  or 

at*- 

in  other  words,  the  ratio  of  modulus  of  elasticities  between  con- 

A 

crete  and  steel,  and  also  on  the  an  ount  of  steel  reinforcemeat 
used. 

Table  8 shows  the  values  of  k and  also  j.  In  this  table,  the 
tensile  resistance  of  the  concrete  is  neglected.  However,  in  the 
sedtion  where  the  concrete  has  some  tensile  resistance  the  value 
of  k becomes  somewhat  larger.  The  formation  of  tension  cracks 
may  change  the  position  and  the  curvature  of  the  neutral  axi s . 
After  a large  diagonal  tension  ha„s  developed  and  arch  actionhas 
developed  to  some  extentinthe  web  of  the  beam  between  the  load 
point  and  the  support,  the  location  of  the  neutral  axis  may  change 
greatly.  Sometimes  it  may  be  possible  that  the  neutral  axis  will 
cut  the  top  surface  in  the  outer  third  of  the  length  of  the  beam 
though  of  course  this  is  not  the  neutral  axis  of  beam  action,  but 
it  may  be  called  the  axis  of  zero  stress. 


TABLE  8 


Value  of  k sjid  j when 

/ Zpri  t pzhz 

n a 7 and  p = 

i 1 

i~n 

« 

J 

)k 

& 

k 

3 

0.1 

.437 

.853 

0.2 

.442 

.850 

0.3 

.447 

.847 

0.4 

.453 

.843 

0.5 

.460 

.839 

0.6 

.467 

.835 

0.7 

.473 

.830 

0.8 

.480 

.825 

0.9 

.488 

.820 

1.0 

.495 

.815 

.0233 


43 


16*  Value  of  Vertical  Shearing;  Stress*-  In  a 
beam  under  flexure,  the  total  tension  in  the  reinforcing  bars 
varies  along  the  length  of  the  beam,  as  does  also  the  total 
compressive  stress. 

The  horizontal  shearing  stress  is  seen  to  be  neces- 
sary in  order  that  the  increments  or  increase  of  the  total 
tensile  stress  in  the  reinforcing  bars  may  be  transmitted  to  the 
corresponding  increments  of  compression  In  the  compression  area 
of  the  concrete,  the  concrete  thus  acting  as  the  stiffening 
web  of  the  beam. 

The  vertical  shearing  stress  is  also  seen  to  be 
necessary  in  order  that  the  increment  of  the  totsl  moment  in  any 
vertical  sections  between  load  point  and  support  may  be  trans- 
mitted to  the  corresponding  increments  of  the  horizontal  stresses 
to  keep  equilibrium  condition.  I’or  this  reason,  at  any  point 

in  a beam,  the  vertical  shearing  unit  stress  is  equal  to  the 
shearing 

horizontal  unit  stress  there  developed. 

If  V^  denotes  the  part  of  the  total  vertical  shear 
which  is  proportional  to  the  resisting  moment  attributed  to  the 
tensile  stresses  in  the  concrete,  then 

88  \ 
bdi 

where  v^  * vertical  or  horizontal  shearing  stress  per  unit  of 
area  in  the  concrete  due  to  V^ 

d^  = distance  from  the  center  of  gravity  of  compressive 

stresses  to  the  center  of  gravity  of  tensile  stresses 
in  concrete. 

And  also  V2  denotes  the  rest  of  the  total  shear,  the  amount 


44 


being  proportional  to  the  part  of  the  resisting  moment  that  is 

due  to  the  tensile  stress  in  the  reinforcing  bars* 

v2  = V2 
'BcT' 

where  v2  = vertical  or  horizontal  shearing  stress  per  unit  of 
area  in  the  concrete  due  to  Vg 
d*  = distance  from  the  center  of  the  reinforcement  to 
center  of  gravity  of  compressive  stresses* 

If  the  tensile  stress  in  the  concrete  is  neglected,  then 


and 


v2  = V 

v = Y 

TTd1 


The  distribution  of  these 
shearing  stresses  is  shown 
in  Pig* 8 

The  calcu- 
lated shearing  stresses 
for  these  two  cases  are  shown 
in  Table  9 • 


(a) 


(b) 


Pig.  8 


45 


The  follov.'ing  calcui&ions  wewre  used  prewiring  Table 
9.  The  bending  moment, 

i2 

> w 1 


3p==fspjbJ: 


0T  T = fsi-Fj-- 

In  the  beams  tested,  p=.0233  b=8in.  d=21in.  l=108in. 


so  that 


“P  = (c» 


0233  yg 
Jo 


bf5 


<b 


I*  Assume  v^=  vg  and-  2k  <1 

for  0*83  kdp  10  in. 

vi  + vg  = .00398P 

for  j=  .85  kd=  9.3  in* 

V1  * Vg  = * 0044P 
II .Assume  v^=  0 v = y,, 
for  3 = .83 
v = . 00289P 
for  j = .85 
v = • 00279P 

In  Table  9,  the  second,  third,  sixth,  and  seventh  columns  have 
been  computed  on  assumption  of  Case  (I),  namely  v^vg.  The 
forth  and  eighth  columns  have  been  calculated  on  the  assumption 
that  V]_=0,  as  in  Case  (II)  above. 


F'3  9- 


. 


c 


Table  9 


46 


Calculated  Shearing  Stresses* 


p » 

= 2V 

3 = 

.83 

3 = 

.85 

vl+v2 

v2 

V 

fs 

Vl+V2 

v2 

V 

fs 

35 

000 

139 

70 

101 

9130 

154 

77 

. ;*5 

9350 

50 

000 

199 

100 

144 

13040 

220 

110 

139.5 

13350 

70 

000 

279 

140 

202 

18260 

308 

134 

195.2 

18700 

100 

000 

398 

199 

289 

25980 

440 

220 

279*0 

26600 

125 

000 

498 

249 

361 

31750 

550  ‘ 

275 

349*0 

33250 

150 

000 

597 

299 

433 

38950 

660 

330 

419.6 

39900 

17*  Direction  of  the  Diagonal  Cracks *-  Cracks 
appearing  in  the  outer  third  have  certain  inclinations  from  the 
vertical  direction  due  to  maximum  stress  line  and  the  farther 
their  location  from  the  load  point,  the  larger  the  inclination 
from  the  vertical  direction*  Table  10  and  Fig*  show  the 
relation  between  inclination  and  distance  from  the  load  point  of 
the  cracks  in  the  beams  tested*  Though  these  data  were  not  enough 
to  drive  conclusive  opinion  they  are  given  out  in  the  hope  of 
throwing  some  further  light  on  this  problem* 

B*  Rectangular  Beams  with  Vertical  Stirrups* 

18*  Notes  of  Test*-  Rectangular  beams  with  4"  spacing 
of  the  stirrups*  Beam  22*3-1*  First  two  small  cracks  appeared 
at  6 in*  and  14  in*  south  from  D*E*L*  at  the  load  of  25  000  lb* 

At  the  load  935  000  lb*  there  were  some  strange  phenomena;  com- 
paratively large  tension  cracks  in  the  middle  third  and  very  small 
diagonal  tension  cracks  appeared  near  the  load  section*  At  the 
load  of  70  000  lb*  the  diagonal  cracks  became  plainly  visible  and 
could  be  traced  about  14  in*  length*  As  it  seemed  impossible  to 
finish  the  test  of  this  beam  that  day,  the  load  was  released  to 


V 


_ A 
• t 


u 


0 o:  *: : 


' ■ 


, ‘ • * 


i ■; 


• •• 

^ V , - i.  . 


/ / 


w 


o : 


* 


) 


* 


')  L ’• 


47 


TABLE  10. 


X)hbanca 

from  t 

J.oqJ  fortf-' 


■ 

Location  of  crack  opening  ama  their  Inclination 


221-1 


221-2 


222-1 


222-2 


E 


-B 


W E 
B S B S 


W 

B S 


E 

B S 


W 

B S 


E 

B S 


W 

B S 


2 

3 

4 

6 70 
8 

10 

12 

14  76 
16 
18 
20 

22  41 
24 

26  33 
28 
30 
32 
34 
36 


95 


* * 

67  84  73 


88 


77 


72  63 


70  74 


88 

95 

75  78  62 

70 


79  90  74  82 


60 


68  58  55  72  54  49  47 

50 

40  43  30  36 

38  44 

34  38  34  43 

38 

32  28  44 

34  32  38 

28  27 

22  22  22 


76 

61 

69 

59 

53 

42 

37 

33 

24  29 

26 
22 


ij0te;  ;J-n^es  0j-  inclination  V/ith  the  horizontal  in  degr 


ees. 


Halation  Between  Inclination 
Of  Cracks  And  Their  Distances  From  Load  Tbinf 


3£ 


y\  j^V'-’vV^^vL  & c\6v^\ , .f': 

Vc?\ ' y.C'.o.A  •:’■••  crV  V^vk  c;;\3v;0 


49 


16  300  lb.  and  left  on  until  Monday,  two  days  after# 

The  readings  were  checked  on  Monday  at  the  load  70  000 
lb*  and  even  the  reading  in  horizontal  reinforcement  could  be 
checked  closely;  the  maximum  difference  was  2000  lb#  per  sq.  in# 
in  the  center  of  the  span# 

At  the  load  of  105  000  lb#  the  maximum  width  of  the 
crack  opening  was  0#01  in.  at  the  S.E#  However,  beyond  this 
load  the  cracks  did  not  open  any  wider# 

At  210  000  lb#  the  diagonal  tension  cracks  seemed  to 
become  smaller  and  the  tension  cracks  in  the  middle  third  became 
large  and  at  the  load  of  214  550  lb#  the  cracls  5 in#  north  from 
south  west  and  6 in#  north  from  south  east  rapidly  opened  wider# 
Then  the  scale  beam  dropped  and  about  1 minute  later  this  tension 
failure  was  followed  by  compression  failure  at  the  top  of  the 
beam  above  these  large  tension  cracks# 

The  final  width  of  this  tension  crack  was  about  0*085  in 
The  load  decreased  to  180,000  lb# 

Beam  22#3-2#  The  first  two  tension  cracks  appeared  at 
the  center  of  the  east  side  2 in#  high  and  2 in#  south  from  the 
H.B.L#  2 in.  high  at  35  000  lb# 

At  the  load  of  50  000  lb#  nine  cracks  appeared  between 
the  middle  third  and  a few  inches  outside  from  it#  Most  of  these 
cracks  were  9 in.  to  11  in#  high. 

The  first  diagonal  tension  cracks  opened  in  S.E#  side 
and  lf#W.  side  at  80  000  lb# 

At  the  load  of  210  000  lb.  the  maximum  tension  crack 
was  widened  to  about  0#01  in#  at  S#W#  side,  and  at  the  load  of 
218  400  lb#  tensilestress  in  the  horizontal  reinforcement  caused 


.0 


. 


failure  at  first  and  was  followed  by  crushing  of  the  concrete  at 
the  top  of  the  beam  above  this  crack*  The  load  decreased  to 
120  000  lb. 

J>.  Rectangular  beams  with  7 in.  spacing  of  the  stirrups. 
Beam  224-1.  This  beam  had  not  a good  surface  on  the  web  and  it 
was  very  hard  to  distinguish  the  cracks. 

A very  small  crack  appeared  2 in.  north  from  S.E.L. 
about  1 in.  high  at  35  000  lb.  At  the  load  of  45  000  lb.  two 
cracks  appeared  6 in.  from  S.E.L.  and  S.W.l.  about  2 in.  high. 

At  the  load  of  55  000  lb.  these  cracks  lengthened  and  a new  crack 
appeared  in  the  middle  third. 

The  first  diagonal  cracks  appeared  at  the  south  side  at 
the  load  of  80  000  lb.  After  this  load,  the  vertical  cracks  did 
not  lengthen  so  much  and  diagonal  cracks  appeared  rapidly. 

At  the  load  of  200  000  lb.  the  maximum  width  of  the 
diagonal  tension  cracks  became  .005  in.  However,  after  this  load 
the  diagonal  tension  cracks  rather  closed  to  some  extent  and 
tension  cracks  in  the  middle  third  developed  rapidly  again,  and 
the  yield  point  of  the  horizontal  reinforcement  was  soon  passed. 
The  failure  caused  crushing  of  concrete  at  the  top  of  the  beam 
above  the  crack.  The  ultimate  load  was  220  500  lb. 

Beam  224-2.  The  first  crack  appeared  at  35  000  lb.  at 
center  about  2 in.  high.  At  the  load  of  50  000  lb.  seven  cracks 
were  observed  in  which  the  first  diagonal  cracks  appeared  14  in. 
south  from  the  S.E.l.  was  included.  At  the  load  of  80  000  lb. 
this  diagonal  crack  extended  about  the  middle  height  of  the  web 


of  the  beam. 


i 1 - 

t • 

. 

* 

r 

► 


51 


After  the  applied  load  reached  90  000  lb*  the  development 
of  tension  cracks  seemed  to  stop  and  at  the  load  of  105  000  lb. 
many  diagonal  cracks  were  observed  at  both  ends  of  the  beam* 

The  beam  failed  by  tension  at  the  load  of  218  000  lb. 
followed  immediately  by  the  crushing  of  the  concrete  at  the  top 
of  the  beam.  The  load  dropped  ■ ^0'1  151  400  lb* 

0*  Kectangular  beams  with  11  in*  spacing  of  the  stirrups* 
Beam  225-1*  Jj'or  this  beam  the  whitewash  made  of  neat  cement  and 
lime  was  so  thick  that  it  was  very  hard  to  find  the  cracks* 

Five  small  cracks,  most  of  them  about  1 in.  high, 
appeared  bet ween  or  a few  inches  outside  the  load  point  at  the 
load  of  35  000  lb* 

Until  the  load  of  50  000  lb*  was  reached  these  cracks 
lengthened  and  became  about  10  in*  high  and  four  new  cracks  also 
appeared. 

A diagonal  tension  crack  was  observed  at  the  load  of 
80  000  lb.  in  the  S.E.  side.  At  the  load  of  200  000  lb.  the 
maximum  opening  of  the  diagonal  tension  crack  in  the  U*W*  side  was 
about  0*01  in* 

At  the  load  of  229  300  lb*  tensile  stress  in  the  horizon- 
tal steel  passed  the  yield  point  and  the  crack  opening  became 
0*09  in.  Crushing  of  concrete  at  the  top  of  the  beam  soon 
followed* 

Beam  225-2.  Four  very  small  tension  cracks  were 
observed  at  the  load  of  35  000  lb*  at  the  center  of  the  span  in 

east  side  and  also  under  the  load  points.  Up  to  the  load  of 
50  000  lb.  ten  new  tension  cracks  distributed  over  the  total 
length  of  the  beam  were  observed. 


52 


The  first  diagonal  cracks  appeared  at  the  load  of 
70  000  lb*  on  S*i^*  side; at  the  load  of  80  000  lb*  many  compara- 
tively large  diagonal  tension  cracks  appeared  near  the  both  ends* 

At  the  load  of  200  000  lb*  the  maximum  opening  of  the 
diagonal  tension  cracks  at  both  ends  was  0*02  in. 

The  tensile  stress  in  the  horizontal  steel  passed  the 
yield  point  at  the  load  of  214  250  lb*  followed  by  compression 
failure  in  the  concrete  at  the  top  of  the  beam  and  the  load 
dropped  to  184  000  lb* 

19*  Rectangular  Beams  with  Vertical  Stirrups*-  The 
first  diagonal  tension  crack  usually  was  observed  at  a load  from 
50  000  to  80  000  lb*  and  in  most  cases  these  cracks  are  short, 
starting  from  one  stirrup  and  ending  at  the  next  stirrup*  As 
the  vertical  stirrups  and  horizontal  bars  kept  the  crack  from 
widening,  there  were  no  crack  openings  larger  than  0*02  inches*. 
However,  there  were  many  diagonal  cracks  developed  as  the  load 
increased,  and  some  of  them  started  from  near  the  support  of  the 
beam  toward  the  load  point. 

The  phenomena  of  the  action  of  the  beams  may  be  consid- 
ered in  three  stages* 

(1)  Tension  crack  stage*  Small  tension  cracks  appeared 
in  the  midspan  or  near  the  load  point  at  loads  between  25  000 
and  50  000  lb*  These  tension  cracks  developed  until  the 
diagonal  tension  cracks  were  observed  on  both  sides  at  the  loads 
between  80  000  and  120  000  lb*  After  this  load  was  reached  the 
development  of  the  tension  cracks  became  very  slow,  and  diagonal 
tension  cracks  appeared  quickly  and  lengthened  as  the  load 


inc reased* 


53 

(2)  Diagonal  tension  cracks  stage.  The  first  diagonal 
tension  cracks  usually  appeared  at  a load  from  60  000  lb.  to 
80  000  lb*  At  the  load  of  80  000  to  120  000  lb.  diagonal  tension 
cracks  were  observed  on  each  side  of  the  beam.  Prom  the  first 
appearance  at  this  load  the  cracks  were  very  long  and  the  length 
of  many  of  them  were  more  than  20  in.  and  developed  rapidly. 

Except  under  the  load  point,  cracks  however  did  not  go 
up  beyond  the  two-third? of  the  total  beam  height.  The  angles 
between  cracks  and  horizontal  reinforcement  are  almost  equal  and 
about  50  degrees.  Such  a large  angle  compared  with  the  angles  of 
the  diagonal  cracks  in  the  beam  without  web  reinforcement  may  be 
due  to  the  fact  that  vertical  shearing  stress  is  transferred  by 
the  web  reinforcement. 

Some  of  these  cracks  first  were  observed  above  the  middle 
height  of  the  web  inclining  upward;  the  lower  part  of  the  cracks 
were  not  observed  until  a few  thousand  pounds  additional  load  was 
applied. 

The  first  cracks  appearing  were  usually  those  nearest  the 
load  point,  and  the  later  cracks  at  increased  load  appeared  near 
the  support.  Dew  cracks  sometimes,  however,  were  seen  between 
these  previous  cracks  as  the  load  increased. 

After  the  diagonal  tension  cracks  prevailed,  the  way  of 
distribution  of  load  may  change,  resembling  that  of  a load  at 
many  points,  and  the  deflection  at  the  center  may  be  relieved  to 
some  extent. 

These  phenomena  continued  until  the  failure  stage  was 


reached. 


. 

. 

. 

- 

. 

. 

, 


•: 

. 

' 


* 


, 


r : - 


< 


> 


(3)  The  failure  stage*  The  failure  of  the  beam  will  come 


in  the  weakest  point  in  the  beam,  either  tensile  stress  in  the 
horizontal  bar;  compressive  stress  or  vertical  shearing  stress  on 
the  concrete  at  the  top  or  vertical  tensile  stress  and  bond  stress 
in  the  concrete  at  the  bottom* 

Most  of  the  beam&tested,  failed  by  tension  at  first*  Afte  • 
a load  from  210  000  lb*  to  220  000  lb*  tension  cracks  in  the  mid- 
span became  suddenly  wide,  and  went  up  very  high  to  the  upper 
part  of  the  web  and  crack  opening  became  about  0*1  in*  to  0*08  in* 
showing  the  yield  point  had  passed* 

At  the  same  time,  diagonal  tension  cracks  seemed  to  be 
suddenly  stopping  increasing  in  width*  Pinal  failure  came  by 
compression  in  the  concrete,  the  resisting  area  becoming  very 
small  and  carrying  load  decreased  suddenly. 

20*  Stress  in  Stirrups.  Diagram  p.l  7 shows  the  unit 
stress  in  each  stirrup.  The  amount  of  stress  transferred  by  the 
stirrups  largely  depends  upon  the  cracks  opened  across  them, 
therefore  the  stress  distribution  in  every  stirrup  is  not  uniform* 
As  usual  cracks  are  wide  near  the  horizontal  reinforce- 
ment, stresses  developed  near  the  bottom  are  the  highest,  and 
their  intensity  is  decreased  toward  the  top  of  the  beam. 

The  stirrups  nearest  the  support  carry  a very  small 
amount  of  stress,  and  even  compressive  stress,  caused  by  concen- 
trated reaction  and  the  stiffness  of  the  beam  was  observed*  The 
amount  of  compressive  stress  in  the  stirrup  varied  as  the  distance 
from  the  support. 

The  stirrups  nearest  the  load  points  also  show  compre- 
ssion at  the  lower  load.  However,  after  the  cracks  crossed  over 
the  stirrup  they  carried  large  tensile  stresses* 


55 

The  maximum  stress  in  the  stirrups  was  usually  observed 
at  the  middle  position  after  the  load  of  150  000  lb.  of  the  outer 
third  of  the  beam  as  the  cracls  develop  most  there. 

Table  II  shows  the  maximum  unit  stress  in  each  side  of 
the  beams  at  the  load  of  200  000  lb.  It  should  be  noted  that  the 
beamS did  not  fail  by  the  diagonal  tension* 

TABLE  11. 

Maximum  Unit  Stress  anxL?  Stress 
in  the  Stirrups  at  the  load  of 
200  000  lb. 

Beam  Bo*  W- c^J~l  E 


Gage  'I/o'.  Un'i'i  Stress  in  Gage  No  * Unit  Stress  in 
Stress  Stirrups Stress  Stirrups 


nr 

’54  & 74  ’ 

W 

SI 

s 

34 

34 

000 

3750 

39 

32 

000 

3530 

223-2 

E 

75 

35 

500 

3920 

79 

30 

000 

3310 

s 

32 

25 

500 

2820 

29 

32 

000 

3530 

224-1 

E 

75 

30 

000 

5900 

79 

26 

000 

5110 

S 

14  & 24 

32 

000 

6280 

29 

28 

000 

5500 

224-2 

E 

75 

30 

000 

5900 

88 

27 

000 

5300 

S 

24 

34 

000 

6680 

29 

29 

000 

5700 

j 

220-1 

E 

74 

30 

000 

9200 

68 

27 

000 

8280 

S 

14 

23 

000 

7060 

28 

24 

000 

7360 

228-2 

E 

74 

31 

000 

9510 

79 

28 

000 

8590 

S 

14 

28 

000 

8590 

19 

27 

000 

8280 

21.  Effect  of  Spacing  of  the  Stirrups.  The  first 
diagonal  cracks  usually  appeared  at  the  load  of  80  000  lb.  In  one 
beam  the  first  diagonal  eraclss  were  noted  at  50  000  lb.  and  70  00C 
lb* 


56 

There  was  no  difference  in  load  at  which  the  first 
diagonal  crack  was  noticed  in  the  hearns  with  different  spacings 
of  the  stirrups. 

The  beams  with  larger  spacings  of  stirrups  have  wide  crack 
openings  at  the  middle  of  the  spacings.  The  maximum  crack 
opening  in  the  beams  with  4 in.  spacing  of  stirrups  was  .01  in. 
and  in  the  beams  with  11  in.  spacing  of  stirrups  was  .02  in. 
However,  the  widths  of  cracks  on  the  stirrups  were  almost  the 
same  with  all  these  beams. 

The  beams  with  closer  spacings  of  stirrups  have  a larger 

number  of  small  cracks  than  the  beams  with  larger  spacings  of 

stirrups.  Perhaps  they  come  from  wider  cracks  giving  some 

relief  in  the  internal  stresses. 

If  the  spacing  is  wide,  the  amount  of  shearing  stresses 

transferred  by  stirrups  becomes  small. 

The  ratio  between  the  observed  maximum  stresses  S and 

total 

calculated  stresses  Sc  are  shown  in  the  table  12.  The  ^ tensile 
in  the  stirrups 

stresses  we re ^ calculated  by  the  following  formula, 

^ -_Z-  .jl. 

where  P = applied  load  in  lb. 


s = spacing  or  4 in.,  7 in.,  and  11  in. 

A = number  of  bars  used  as  the  stirrups  = 
S = 5740®  for  4 in.  spacing 
= 10  075s  for  7 in.  " 

* 1578*  for  11  in.  " 

5 = .85 

TABLE  IS. 

Ratio  between  Observed  and  Calculated  stirrups  Stress. 


Beam  Ho. 

s 

Load 

m 

S/Sc 

209000  lb. 
S 

s/s0 

225-1 

. it 

5510 

.577 

<S 

5550 

.615 

; s 

5750 

.654 

N 

5420 

.596 

225-2 

• IT 

5920 

.690 

s 

5550 

.615 

rt 

. . b 

2820 

.487 

11 

5510 

.577 

224-1 

. 11 

5900 

.586 

q 

It'S 

5500 

.546 

; S 

6280 

.625 

IT 

5110 

.507 

224-2 

11 

5900 

.586 

S 

5700 

.566 

. s 

6680 

.605 

IT 

5500 

.526 

225-1 

Li 

9200 

.582 

rt 

O 

7560 

.466 

; s 

7060 

.447 

H 

8280 

.524 

225-2 

/ U 

9510 

.60S 

3 

8280 

.524 

S 

8590 

• 544 

7 

8590 

.544 

S2.  Effectiveness  of  Vertical  Stirrups. - Action  of 


stirrups  for  the  diagonal  tension  is  analyzed  in  Section  4 and 
phenomena  of  test  show  the  general  agreement  with  that  analysis. 

Additional  strength  due  to  stirrups  is  4O7&  at  the  load  of 
failure.  The  highest  stress  in  the  stirrups  was  observed  in  the 
Beam  Ho.  22,  5-2  and  was  55  500  lb.  However  this  is  not  the 


failed  by  diagonal  tension* 


C.  Tee-beams  with  Vertical  Stirrups 


59 


23,  Notes  of  Test, - 

(a)  Tee-beams  with  4-in,  spacing  of  stirrups. - 

Beam  226-1,-  This  beam  was  dropped  from  a height  of 
about  7 ft,  while  handling  by  crane  7 days  after  being  made. 

At  the  load  of  25  000  lbs,  no  cracks  appeared. 

The  first  tension  cracks  appeared  10  in.  south  from 
N.E.L,  about  2 in.  high  at  35  000  lbs.  At  50  000  lbs.  7 
cracks  were  distributed  between  the  load  points  or  along  the 
stirrup  near  the  load  points. 

At  the  load  of  70  000  lbs.  three  new  cracks  appeared, 
two  of  them  on  N.W.  side. 

The  first  diagonal  crack  was  observed  near  the 
middle  part  of  the  S.E.  side  at  the  load  of  80  000  lbs.,  and 
at  the  load  of  14  000  lbs.  a crack  reached  1 in.  high  in  the 
flange  under  the  S.E. I*. 

When  the  load  of  .259000  lbs.  was  reached  the  tension 
cracks  became  large  and  just  before  the  measurements  o f de- 
formation at  this  load  were  started,  a big  noise  with  shock 
was  heard  and  the  load  dropped  to  222  500  lbs.  By  further 
loading,  the  beam  showed  itself  able  to  carry  the  load  of 
262  340  lbs.,  when  the  second  shock  occurred  and  the  load 
dropped  to  M 240  000  lbs.  On  the  third  loading,  at  the  load  of 
252  000  lbs.,  tension  failure  was  completed  and  the  load 
dropped  to  154  300  lbs.  and  the  beam  could  not  carry  any  further 


load 


. J . • \ 


\ 


60 


Beam  226-2.-  In  this  beam  there  were  many  holes  under 
the  horizontal  reinforcing  bars. 

The  first  crack  was  observed  10  in.  south  from 
N.E.L.  about  1 in.  high  at  the  load  of  35000  lbs.  Until  the 
load  of  50  000  lbs.  eight  cracks  were  seen  and  some  of  than 
reached  about  12  in.  high,  also  a horizontal  crack  appeared  at 
N.E.  side. 

At  the  load  of  60  000  lbs.  the  first  diagonal  tension 
crack  appeared  nearly  at  the  center  of  the  web  on  the  U.E. 
side.  Tension  cracks  in  the  midspan  of  the  beam  developed  and 
some  of  them  reached  the  height  of  13  in.  After  the  load  had 
reached  80  000  lbs.  tension  cracks  did  not  lengthen  and  diagonal 
tension  cracks  developed  rapidly.  Beyond  trie  load  of  200  000 
lbs.  tension  cracks  opened  widely  especially  after  the  load  of 
220  000  lbs.  At  the  load  of  240  000  lbs.  it  was  believed  tnat 
failure  might  come  by  the  tensile  stress  passing  the  yield 
point  of  the  horizontal  bars,  and  the  maximum  crack  opening  at 
this  load  was  0.06  in.  at  the  center*  The  final  failure  was 
caused  by  the  crushing  of  the  concrete  at  the  north  support, 
load  dropped  to  140  100  lbs.  Average  bearing  stress  on  the 
support  was  3 110  lbs.  per  sq..  in. 

(b)  Tee-beams  with  7 in.  spacing  of  the  stirrups. 

Beam  227-1.-  At  the  bottom  of  the  beam  the  surface 
was  very  rough.  While  putting  this  beam  upon  the  machine  a 
piece  of  concrete  was  broken  off  the  under  side  of  the  beam 
at  the  support  at  the  south  end.  A fair  bearing  , however,  was 


secured 


61 

The  first  small  tension  crack  occurred  at  50  000  lhs. 
2 in,  north  from  S.E.L.  1.5  in.  high.  With  the  load  60  000  lb 
had  reached  two  big  cracks  appeared,  one  2-in.  south  from 
S.E.L.  12-in.  high,  and  the  other  2 in.  north  from  N.E.L.  12  in 
high. 

At  the  load  of  70  000  lbs.  the  first  diagonal  crack 
was  developed  10  in.  south  from  S.W.L.  Up  to  10  in  high  until 
the  nearest  stirrup  from  the  load  on  this  side.  However, 
no  diagonal  tension  cracks  appeared  in  the  west  side  until 
the  load  of  90  000  lbs.  was  reached. 

Beyond  120  000  lbs.  vertical  tensile  cracks  seemed 
to  develop  very  slowly  and  diagonal  tension  cracks  extended 
quickly. 

Beyond  200  000  lbs.  tension  cracks  revived  and 
diagonal  cracks  seemed  not  to  grow  and  failure  was  expected  to 
be  caused  by  failure  of  horizontal  reinforcing  bars.  At  the 
load  of  250  000  lhs.  diagonal  cracks  at  north  side  became 
large  and  also  on  the  bearing  plate  of  the  south  end  support, 
chipping  cracks  were  observed  accompanied  by  a small  noise  and 
diagonal  tension  cracks  at  this  south  end  became  large. 

The  beam  carried  the  load  261  300  lbs,  when  south 
end  of  the  beam  suddenly  broke  off  without  any  big  noise. 

After  failure  it  was  found  that  the  middle  horizontal  bar  in 
the  bottom  layer  had  been  broken  near  the  beginning  of  the 
hook.  This  might  be  caused  by  the  accident  in  putting  the 
beam  into  the  machine  just  before  the  test. 


62 


Beam  227-2. - The  first  crack  appeared  at  the  center 
of  the  west  side  1 l/2  in.  high  at  the  load  of  35  000  lh. 

At  the  load  of  50  000  lbs.  nine  cracks  developed  and  some  of 
them  lengthened  more  than  14  in. 

The  first  diagonal  tension  cracks  appeared  at 
80  000  lbs.  on  both  of  S.W.side  and  N.E.side. 

After  the  load  of  230  000  lbs.  was  reached  tension 
oracks  in  the  midspan  became  large  and  at  240  000  lbs.,  tensile 
stress  in  the  horizontal  reinforcement  passed  their  yield 
point,  and  tension  cracks  opened  wider.  However,  the  beam 
carried  the  ultimate  load  of  268  600  lbs.  Then  with  a shock 
and  a noise  the  load  dropped  to  238  600  lbs.  immediately.  Upon 
the  application  of  the  further  loading,  this  beam  could  carry 
the  load  of  266  300  lbs.  when  the  secondary  failure  came  on 
the  north  end  of  the  beam  caused  by  the  crushing  stress  in  the 
concrete  on  the  support  accompanied  by  the  compression  failure 
at  the  top.  Load  dropped  : to  224  300  lbs. 

(c)  Tee-beams  with  11  in.  Spacing  of  Stirrups. 

Beam  228-1.-  At  the  load  of  50  000  lbs.  five  cracks 
appeared  suddenly;  one  of  them  at  the  center  of  the  beam  on 
east  side  10  in.  high,  the  rest,  along  the  nearest  stirrups 
from  the  load  points,  all  of  them  about  14  in.  high. 

At  the  load  of  60  000  lbs  nine  new  cracks  appeared 
distributed  all  over  the  beam  from  8 in.  to  12  in.  high. 

The  first  diagonal  tension  crack  appeared  at  the 
south  side  at  the  load  of  70  000  lbs. 

Beyond  the  load  of  120  000  lbs.  the  tension  cracks  did 
not  lengthen  and  diagonal  tension  cracks  developed  very  greatly 


' 


' 


63 


At  the  load  of  220  000  lbs.,  the  largest  diagonal  tension  cracii. 
at  the  N.E.side  opened  ,0026  in. 

Beyond  the  load  of  240  000  lbs.  tension  cracks 
became  larger  rather  quickly.  A noise  was  heard  at  the  load  of 
260  900  lbs.  and  tension  cracks  in  the  midspan  opened  wide 
followed  by  another  large  vertical  crack  and  horizontal  crack. 
The  load  dropped  to  241  200  lbs.  The  beam  carried  an  ultimate 
load  of  264  E00  lbs.  and  then  crushing  failure  at  the  north 
end  on  the  support  accompanied  by  diagonal  tension  failure 
completed  the  final  failure  of  the  beam  and  the  load  dropped 
to  146  400  lbs. 

Beam  228-2.-  At  the  load  of  35  000  lbs.  the  first 
two  cracks  were  observed  at  E side:  one  2 in.  south  from 
S.E.l.  under  the  stirrups  and  the  other  2 in.  north  from  N.E.L. 
along  the  stirrups  10  in.  high. 

Six  new  cracks  appeared  between  and  under  the  load 
points  and  most  of  them  extended  about  13  in.  high. 

At  80  000  lbs.  the  first  diagonal  tension  cracks 
started  to  appear  at  N.E.side.  At  the  load  of  90  000  lbs.  a 
big  diagonal  tension  crack  appeared  at  S.E.side,  and  at  the 
load  of  105  000  lbs.,  a crack  was  found  even  in  the  flange 
in  S.W.  side. 

At  the  load  of  250  000  lbs.  diagonal  tension  cracks 
became  so  wide  as  0.0510. 

At  the  load  of  260  000  lbs.  tension  cracks  near  the 
north  side  load  point  became  very  large  and  the  opening  of  the 
crack  was  0.06  in.  at  10  in.  high  from  the  bottom  and  at  the 
bottom  under  the  H.W.L.  was  0.1  in.  Boad  dropped  until 


64 

235  400  lbs.  Upon  further  loading  the  beam  failed  at  a load 
of  255  200  lbs,  caused  by  compressive  stress  in  the  concrete 
at  the  top.  The  load  dropped  to  236  100  lbs. 

24.  T-shaped  beams  with  vertical  stirrups. - 
The  first  diagonal  tension  cracks  usually  appeared  at  a load 
from  60000  to  80  000  lbs.  and  there  were  no  apparent  difference  , 
of  the  amount  of  load  and  the  way  of  formation  of  cracks 
between  T-b earns  and  rectangular  beams. 

The  phenomena  of  carrying  load  may  also  be  divided 
into  three  stages  and  the  stages  are  almost  the  same  as  in 
rectangular  beams  except  the  last  stage.  (See  Section  19) 

The  last  stage  was  observed  beyond  the  load  of  230000 
lbs.  to  260  000  lbs,  the  higher  load  being  caused  by  the 
higher  position  of  the  neutral  axis  in  this  type  of  beam, 
and  the  greater  concrete  area  at  the  top  which  was  large 
enough  to  prevent  secondary  failure  by  compression.  The 
oarrying  load  was  19  per  cent  higher  than  that  of  the  rectangu- 
lar beams,  and  the  value  of  j was  also  7 per  sent  larger. 

As  the  diagonal  tension  stage  was  longer  in  T-beams 
thhn  rectangular  beams  diagonal  tension  cracks  appeared  more 
in  these  beams.  The  cracks  that  appeared  at  these  higher  loads 
started  from  the  end  of  the  span  either  from  the  bottom,  or 
from  the  middle  height  of  the  web  extending  both  downward  and 
upward.  Some  of  them  formed  curves  having  a smaller  radius 
of  curvature  than  those  occuring  at  the  lower  loads,  the  latter 
being  as  nearly  straight  and  making  an  angle  of  about  50 
degrees  with  the  horizontal  reinforcement. 


65 

The  reaction  at  the  support  was  so  great  that  most 
of  the  secondary  failures  took  place  at  the  bearing  on  the 
support.  The  craclJ^^p eared  at  this  stage  showed  larger 

angles  than  the  craok^1^^) eared  in  the  former  stages. 

A 

The  tension  cracks  also  extended  so  high  that  some 

of  the  beams  failed  by  secondary  crushing  at  the  top  of  the 

. ,qx  the 

middle  span. 


. 


66 


25.  Stress  in  Stirrups."  Diagrams  show  the  unit 
stress  and  total  load  of  each  stirrup. 

The  stress  distribution  in  stirrups  of  T-beams  is  more 
irregular  than  in  the  rectangular  beam,  and  maximum  stresses 
were  generally  observed  at  the  middle  height  of  the  beam. 

Since  the  flange  is  stiffer  than  the  web  the  effect  of  arch 
action  is  to  move  the  maximum  stress  line  up  a little.  Strain 

gage  readings  on  the  stirrups  near  the  supports  showed  that 

the 

while  they  had  no  cracks  across  the  stirrups, nearest 

K 

stirrups  were  carrying  compression  during  the  greater  part  of 
the  test.  This  was  due  to  the  stiffness  of  the  flange  and 
concentrated  shear  at  the  support. 

The  stirrups  nearest  the  load  points  show  sometimes 
compression  at  the  lower  loads.  However,  as  the  vertical 
cracks  along  the  stirrups  appeared'  at  a load  of  about  50  000  lb. , 
the  stirrups  carried  a great  deal  of  tensile  stress. 

The  stresses  in  stirrups  in  T-beams  were  somewhat 
larger  than  the  stressed  stirrups  in  rectangular  beams.  A singl  i 
large  crack  is  more  dangerous  than  many  cracks  crowded  together. 

At  the  load  of  26  000  lb.  the  gage  line  Ho. 14  in  the  beam  228-1 
showed  the  unit  stress  of  44  500  lbs. 

The  table  shows  the  maximum  unit  stress  on  each  side  of 
the  beams  at  the  load  200  000  lb.  It  should  be  borne  in  mind 
that  the  beams  did  not  fail  by  diagonal  tension. 


67 

TABLE 

13 

» 

Maximum  Unit 

Stress 

“Stress 

in 

the  Stirrups  at 

the  Load 

of 

200000 

lb. 

Beam 

Bo. 

W- 1 

E - 

Gr 

age  Bo. 

Uni t Stress 

Stress 

in 

Stirrups 

Gage 

Bo. 

Unit 

Stress 

Stress 

in 

Stirrun 

226-1 

63 

iv/.-*- 

32  500 

7b 

'3  590 

69 

W 

30  000 

ib. 

3 310 

S - 

23 

27  000 

2 980 

19 

30  000 

3 310 

226-2 

B 

53 

31  000 

3 420 

78 

26  000 

2 870 

S 

13 

28  000 

3 090 

19 

31  000 

3 430 

227-1 

B 

84 

35  000 

6 870 

89 

33  000 

6 480 

S 

14 

«6  000 

4 910 

39 

39  000 

7 660 

227-2 

B 

73 

31  000 

6 090 

88 

32  500 

6 380 

S 

25 

23  000 

4 520 

20 

30  500 

5 990 

228-1 

B 

63 

24  500 

7 520 

68  & 80 

19  000 

5 830 

S 

14 

31  000 

9 520 

19 

29  000 

8 900 

228-2 

B 

63 

29  000 

8 900 

80 

23  000 

7 060 

S 

23 

29  500 

9 050 

29 

33  000 

10  150 

68 


26*  Position  of  Neutrtl  Axis*-  Analysis  for  the 
location  of  neutral  axis  in  the  T-heam  using  the  parabolic 
formula  may  be  shown  as  follows: 


Fig.10. 

y=  o-f 

Aria  = ±(l- W Ec 

fc  = ('~ ~2% ) a 

fc  = 0- '2'%vr')  Ec4c  m 


Now  compression  in  flange  = shaded  area 

(k'-bjd  (I  - 

”irEc£t  (k'-bj 

Equating  horizontal  tension  and  compression. 

A^s  s6  = ^-(i'3|)^c£ckcJb  ■+  [(1-^)  ~(l~j  %'*■)  k 


Now 


and  put 
then 


a 


nd 


=-K. 


wut_JL 


69 


From  these  equations  

1 Fit 

The  value  of  k in  the  different  stages  of  resistance  are  shown 

in  Table  14. 

TABLE  14. 

Location  of  the  neutral  axis  in  T-beam 

Q[  .1  .2  .3  .4  .6  .6  • 7 .8  .9  .10 

k .312  .309  .307  .306  .306  .306  .305  .305  .304  .304 
kd  6.56  6.49  6.45  6.42  6.42  6.42  6.40  6.40  6.39  6.39 

As  the  location  of  neutral  axis  is  very  near  the  bottom 
of  flange,  the  formula  for  j in  rectangular  beams  may  apply 
without  any  objection. 

3 = 1 - I (1  + ? ) K 

TABLE  15. 


V - n n 

q .1  .2 

.3  ' .4 

.5 

.6 

.7 

.8 

.9 

.10 

JC  .312  .309 

.307  .306 

.306 

.306 

.305 

.305 

.304 

.304 

3 .895  .895 

.895  .894 

.893 

.892 

.891 

.889 

.888 

.886 

27.  Effect  of  Spacing  of  the  Stirrups."  Variation 
in  the  spacing  of  stirrups  did  not  show  any  large  difference 
in  the  load  at  which  the  first  diagonal  cracks  appeared.  The 
first  crack  generally  appeared  at  a load  of  about  70  000  lb. 

The  effect  of  spacing  of  the  stirrups  upon  the  crack: 
formation  is  almost  the  same  as  that  with  the  rectangular  beams. 


/ 


1* 


70 

The  beams  with  larger  spacings  have  wide  crack 
openings,  while  width  on  the  stirrups  are  almost  same. 

The  beams  with  smaller  spacing  of  stirrups  have  more 
cracks  than  that  with  larger  spacings  as  is  the  case  in 
rectangular  beams. 

As  the  stresses  in  stirrupe depend  greatly  upon  the 
position  of  large  cracks  and  since  the  location  of  cracks 
was  very  irregular  in  the  T-beams  the  same  conclusions  on 
the  effect  of  stirrups  in  the  rectangular  beams  could  not  be 
applied  to  this  type  of  beam. 

The  ratio  between  the  observed  maximum  stress  S and 
calculated  stress  Sc  was  obtained  in  the  same  way  as  with 
rectangular  beams  using  the  value  of  j - ,89  as  shown  in 
Table  16. 


71 


TABLE  16. 

stresses 

Maximum  ^bseived  nd  calculated*11  the  stirrups  at  the  load  of 

2(6  000  lbs.  A 


__NOXjfc2l 

South 

S/Sc 

S 

S/Sc 

226-1 

W 

3590 

.671 

2980 

.557 

E 

3310 

.619 

3310 

.619 

226-2 

W 

3420 

.639 

3090 

.578 

E 

2870 

.556 

3430 

.641 

227-1 

W 

6870 

.734 

3910 

.524 

E 

6480 

.692 

7660 

.818 

227-2 

W 

6090 

.650 

4520 

.483 

E 

6380 

.681 

5990 

.640 

228-1 

W 

7520 

.512 

9520 

.649 

E 

5830 

.397 

8900 

.605 

228-2 

W 

8900 

.606 

9050 

.616 

E 

7060 

.481 

10150 

.690 

. ' 


72 


Rectangular  Beam  with  Bent-up  Bars, 

28,  Rotes  of  Test, - 

Beam  229-1.-  The  side  £uces  of  this  beamvy&re 

slightly  inclined  frcm  the  vertical.  Ro  cracks  had  appeared 
at  the  load  of  40  000  Its.  At  the  load  of  50  000  lb. 
twelve  cracks  appeared  at  once,  some  of  tnem  reached  10  in. 
high.  At  the  load  60  000  lbs.  most  of  these  cracks  had 
lengthened  and  seven  new  cracks  appeared  in  various  parts  of 

the  beam  even  22.7  in  south  #from  the  S.W.L.  Large  diagonal 

a 

c^eks  were  observed  on  north  side  caused  probably  by  the 
slipping  of  the  bent-up  bar.  The  maximum  crack  opening  on 
this  side  was  0.028  in. at  the  load  of  200  000  lbs. 

The  failure  was  a tension  failure  in  the  horizontal 
reinforcement,  followed  a compression  failure  at  the  top 
of  the  beam.  The  ultimate  load  was  225  400  lbs.,  decreasing 
to  181  500  lbs. 

Beam  229-2.-  At  the  load  of  50000  lbs,  the  first 
ten  cracks  appeared, distributed  between  points  of  bent  up 
bars. 

At  80  000  lbs.  cracks  along  the  bent-up  bars  were 
observed  at  the  south  side.  At  the  load  of  105  000  lbs,  many 
cracks  had  appeared  all  over  the  beam. 

At  the  load  of  200  000  lbs.  deformation  of  the 
concrete  under  and  near  the  S.S.L.  increased  rapidly,  showing 
the  failure  of  concrete  was  near.  The  beam  failed  by  the 
crushing  of  the  concrete  at  the  load  of  213  700  lbs.  and  the 
load  dropped  to  189  000  lbs. 


73 

29.  Rectangular  beams  with  Bent-up  Bars.-  Only 
two  beams  of  this  type  were  tested.  Two  bars  were  bent-up 
for  shear  reinforcement,  one  at  6 in.  and  the  other  at 
15  in.  from  the  load  point. 

The  diagonal  tension  cracks  were  observed  at  the 
load  of  60  000  lbs.  in  beam  Ho.  229-1  and  50  000  lbs.  in 
beam  Ho.  229-2.  Therefore,  it  seems  safe  tosay  that  diagonal 
tension  cracks  in  this  type  of  beams  may  be  observed  at 
a somewhat  smaller  load  than  in  beams  with  all  horizontal 
bars  straight. 

In  studying  the  load  carrying  phenomena  it  may  be 
better  to  divide  the  work  into  three  stages  as  was  done 
in  the  beams  with  vertical  stirrups,  though  the  stages  are 
not  as  definite  as  the  case  of  the  beams  with  stirrups. 

Even  in  the  diagonal  tension  stage,  a few  more 
vertical  cracks  opened  in  the  middle  third  of  the  span. 

At  the  higher  load  many  curved  cracks  appeared 
near  the  end  of  bent-up  bars. 

The  crack  openings  were  wider  than  those  of 
beams  with  vertical  stirrups  and  the  maximum  width  observed 
was  .028  in.  at  the  load  of  200  000  lbs.  in  Beam  229-1. 

The  last  stage  started  at  the  load  of  about  200  000 
lbs.  Both  beams  failed  by  tension  in  the  steel  at  the 
center  of  the  span,  followed  by  compression  failure  at  the 
top. 

The  ultimate  load  for  Beam  Ho.  229-1  was  225  400  lbs. 


and  for  Beam  Ho.  229-2  was  213  700  lbs 


. 


r : , « ‘ 

. 

c 


Taking  average  value  of  these  ultimate  loads  the 
average  shearing  unit  stress  for  these  "beams  is  789  Its,  per 
sq.  in.  if  the  value  j is  assumed  to  he  .83  as  in  the  other 
type  of  rectangular  beams. 


. 

. ' 


. 


75 


30*  Conclusions.-  The  foregoing  discussion  may 
he  summed  up  in  the  following  conclusions: 

I.  In  deep  beams  with  short  span,  high  diagonal 
tensile  stresses  can  be  developed. 

II.  In  these  tests,  beams  without  stirrups  carried 
an  average  shearing  unit  stress  of  525  lbs.  equal  to  0.12  fc*. 

III.  Hooks  at  the  ends  of  bars  are  effective  in 

preventing  slipping  of  bars,  and  it  is  desirable  to  have 
hooks  at  the  ends  of  the  bar  even  when  corrugated  bars  are  used. 
These  hooks  are  evidently  essential  to  the  development  of 
high  shearing  stresses.  v 

IV.  Beams  without  web  reinforcement  failed  by 
either  (1)  shearing  or  breaking  of  the  concrete  at  the  top 
near  the  load  point  or  (2)  vertical  tension  or  stripping  of 
the  concrete  above  the  reinforcing  bars  and  near  the  diagonal 
tension  cracks. 

V.  After  diagonal  tension  cracks  developed  the 
tension  cracks  in  the  middle  which  had  appeared  before  did 
not  develop  rapidly. 

VI.  At  the  final  failure  stage,  when  the  beam 
failed  by  tension  in  the  steel,  the  diagonal  tension  cracks 
did  not  develop  rapidly. 

VII.  Vertical  stirrups  are  effective  in  preventing 

v 

crack  widening  and  also  in  transferring  shearing  stress.  In 
the  beams  tested,  the  resisting  strength  was  increased  at 
least  40  per  cent  by  the  use  of  vertical  stirrups  though  as  the 
beams  failed  by  tension  in  the  horizontal  reinforcement  the 


76 

full  effectiveness  was  not  developed, 

VIII.  The  beams  with  the  closer  spacing  of 
stirrups  had  a larger  number  of  small  cracks  than  the  beams 
with  the  larger  spacing  of  stirrups, 

IX.  The  beams  with  the  larger  spacing  of  stirrups 
had  wider  crack  openings  midway  between  stirrups  than  the 
beams  with  the  smaller  spacings  of  stirrups, 

X.  In  the  rectangular  beams,  as  the  spacing  of 
stirrups  increased  the  amount  of  shearing  stress  transferred 
by  stirrups  decreased  slightly, 

XI.  For  stress  in  stirrups  the  coefficient  C in 

the  formula  J-C  was  found  to  be  a little  less 

than  2/3.  Therefore,  2/3  can  be  used  for  practical  purposes 
even  in  a deep  beam. 

XII.  The  effect  of  spacing  of  stirrups  in  T-beams 
is  almost  the  same  as  in  rectangular  beams.  However,  the 
crack  formation  is  more  complicated  and  irregular  in  the 
T-beams.  Therefore,  the  position  of  maximum  stress  in  stirrups 
is  also  irregular,  and  the  value  is  somewhat  higher  than  in 
rectangular  beams. 

XIII.  The  diagonal  tensile  stress  distribution 

in  T-beams  was  almost  the  same  as  in  rectangular  beams.  How- 
ever, the  diagonal  tension  stage  is  longer  in  T-beams  than  in 
rectangular  beams. 

XIV.  The  T-beams  carried  an  average  of  19  per  cent 
higher  load  than  the  rectangular  beams. 


. 

- 

* 


* 


< 

. 

- 

. 

< 

- 


77 


XV.  In  the  T-b  earns  the  coefficient  G in  the 
formula  3 ~ va**ies  more  than  in  the  rectangular 

beams^and  in  one  beam  the  value  of  C was  considerably  greater 
than  2/3. 


XVI,  A concentrated  large  crack  is  more  dangerous 
than  a number  of  distributed  cracks.  Such  a single  concentrated, 
crack  may  be  caused  by  non-homogeneity  of  the  beam  or  by  wide 
spacing  of  stirrups;  the  formation  of  a number  of  smaller 
cracks  may  be  produced  by  homogeneity  of  material  or  by  well 
spaced  and  distributed  stirrups. 

XVII.  Bent-up  bars  are  effective  in  preventing 
widening  of  cracks  and  also  in  transferring  shearing  stress. 

The  resisting  strength  added  by  bent-up  bars  in  the  one  type 
of  beam  tested  was  at  least  40  per  cent  of  the  ultimate  strength 
of  the  beams  without  web  reinforcement.  The  full  effect  was 
not  developed,  since  the  beam  failed  by  tension  in  the  hori- 
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Gage  Line  Numbers  in  Beam  No.  22.2 

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5 

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N 


125  |23  12.1  119  |I7  IIS  113  III  |09  l°7  105  |03  lot 

00  0000000000000000  000000  0,  00 

124  122  i2o  iis  iis  m4  ji*  mo  iog  loft  io4  io2 


Gaq<z  Line  Numbers  inBeamNo.22. 
EAST  3/de. 


201  203  205  207  209  2M  21 3 2lS  2(7  2/9  221  223  22  S 

O 0 0,0  0 0 00  0,0009  oooo  OOO  QOQ  ooo  o 

202.  234  20 6 208  210  2/2 24 2J6 2j6 220  222 224 


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(25  123  121  h9  M7  US'  ii3  IK  109  107  105  103  |o| 

OO  QOOOOO  OOO  OOOOOOOOOOOOOOOO 

1X4  i V2.  \Z0  \\&  ng  tt4-  HZ  no  108 106 | o4- log. 


Gca\<z  V20 


118 

Gage  L ine  Numbers  in  BeamNo,22.3-Z 

EAST  SIDE. 

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pf 

o 

0 

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O 

76 

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62 

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63 
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64 
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52 

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53 

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54 

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34 
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00l£4  00I22  Oo/20  O 0u*  0 116  O H4  O H2  O iro  O 108  Ool06  00l°4  Oo'^Oq 


Gage  Line  Numbers  in  Beam  No.22,3-1 


EASTSTIDE 


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17 

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18 
o 

19 

o 

20 


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26 

O 

27 
O 

28 
O 

29 
O 

30 


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36 
O 

37 
O 

38 
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39 
O 

40 


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o 

■57 

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58 
o 

59 
o 

60 


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66 

6 

67 

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63 

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69 
o 

70 


o 

76 

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77 
O 

78 
& 

79 
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80 


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86 

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87 
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88 

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69 

o 

90 


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N 


o 

81 

o 

82 

o 

83 
o 

84 
o 

85 


O 

71 
O 

72 
o 

73 
O 

74 
O 

75 


O 

61 

O 

62 

o 

63 
O 

64 
O 

65 


O 

51 
O 

52 
O 

53 
O 

54 
o 

55 


O 

31 

0 

32 
O 

33 

o 

34 
0 

35 


O 

21 

O 

22 

O 

23 
O 

24 
O 

25 


O 

11 
O 

12 
O 

13 
O 

14 
O 

15 


O 125  oO  I23qO  121  oO  119  oO  IIT  O \\5  O 113  O III  O 109  O o 107  O o l°5  O o 103  O O 1° 1 o 


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37 

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...  . . V . : Jj 


C c ::  fs.3  U).  i < 5^  3, 


r^\;vo:v^sv'z  vo, 


Unit  in  Thousands  of  Pounds. 


is: 

30 

2.0 


10 


OOP  OOP  Ib5 


20 


lETOOQ  0 IP5- 


10 


105000  IbT 


10 


TO  OOP  Ito. 


5-. 

0 


35000  I la?- 


c>qg/  in  pounds 


132 


Unrh  5-J-r<Z55  in  J^/rrupS.  /m.^Zoooo  /b. par  sy.  in. 


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Oi  <i 


p-l  D ‘WftwS 


v>  Q 
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■J  O 0 0 cl 


CjQGODI 


iitfOU?. 


<s;  $ 

\ f A 

ft  ft  A • * ft c- 


a 


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>:•  c *A* 
C X -X 


Un'/fdfrossin  Thousands  of -pounds. 


/' 


\ 


a 0,00  0,0's 


oe 


w . 


f 


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or 

sc;  c.oooci 


v.  --ti.* 


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i ? a EA-feJi 


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tql  0C\>8f;S  . J'J  ‘v'SJS  ri  W 


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UnifPfross  in  Thousands  of  Pounds. 


^ r r 

'.s  - 


r 


° ° ^ /'•-,%  ' > ' w ' • 
c C*,  O •<-£*»•  ..-.*?•  ’".-7  ° 'c 

■-  - ' 'r  ,.'  " ? ,.  ^ 7:  *■<  '.^'  ••  ° 

■ i . '--  'V  ■ * ' ' *•■ 

7 '/%/ H.J  :sr'1  ?”Ok\  '74)7 


c.  is  O 
..  <sto 


O 

o 


A 

5 


■“T"“ 


. ,.:•]].  ^ • ,7  J.U 


IT'  6 


2ooooo 


150000 


I00O0O 


50000 


81  A82  A 83  k 84  >85 


200 0O0 


200000 1 


l50  000f 


iooooo' 


0 

1 22 

I23  , 

Unrf~  /n  Sf/rf^up^  / *n,  = 20000  /&.  p<tr  C5^.  /n . 

22,3-2.  W. 


a ..[ 


i 


6 

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i 


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0 GOCtf'O^ 

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\ 


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\ 


V 


\ 


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c> 

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qoooo; 


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4-M  X 


0 

Si.'; 


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\ 


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6 ' 1 6 £'  • ' 6 ' S&  X 


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\ 


• -XW'y'x  :C  u\  <t;  . v'v  v.r.v’» 


.V 


Load  in  ^ pound 


137 


L/niL  $-n255  //?  O/irrups  /in.  = 2o  ooo  lt>.  par$^.  m. 


Z 2,3-2  W. 


t 


o- 


_,tv.  r-~v  'a.  d\  •oo.o'.'J.S:  ••  .cV  \V*. 


Unit  Jfrejj  in  lhousanc/5  of  Pounds. 


;X 


"O'— Q. 


.fccs;  OOOOOS, 


V 


"c 


/ 


/ 


1 


,o  — ■ “•  -a, 

WIOOO0S!  ' <: 


\ 


\ 


Ok 


> i 


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j / 


oi 


— ... 


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f 


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\ 


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V 


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cr'' 


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.sal  ooo  dc 


c> 


X- - Vi  'V-  j^V-a^V^Yl  X UpCV. 


Unit  Stress  in  Thousands  of  Pounds. 


• ■% 


30 


ZO 


to 


2000  OO  lbs. 


20 


10 


15000  o tbs. 


105000  It73. 


10 


70  000  lb y. 


5 

0 


35  000  Ifrx 


E.  223-2  U.L.  ZI3000  L&s. 


911 


/ \ 


/ A 


05 


", 

; V / 

//  1 


/ 


T3 


, / / 7 

A / ■' 

7 / 7 

//  ,y 


CCJ!  OG  0 GOS 


.•Cdi  COOQcl 


,-v- 


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/ 


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A 

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usT^  \ 


~yf~~ 


01 


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S^G;-;..,' 


?.«;  oo-o 


■" 

d - '-, 

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_ i -luSiG.,. -j-=h _■ 


d!  C OO  if. 


.:':--vsafo 


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o n o 
o Oo«up;3  A 


,v*>-  ' • . .\ 


• \v  ••  y* 


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CJi< 


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c~u  - - ’ - 


o 


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y.  x,! 

. ••  - ;>  o A\c  ' . c -•  ,.c< 

. - c 


/ s/{  fh**  •\  -j  i v 

z/^  # 77  A ■ V Nr-t 


51 


»..«»i>jiin  in.*  «■— .-w~  .■■'»»w  • 


s?.cn  oOva>;::  .j .u  m-sss 


<A\YyA:A2.y  \vs  ^oe- 


unoc/  v/ 


140 


lOOOOl 


50000 


C\ 

Y 

A 

1 6 /“ 

2.00000 


87 


76  A 77 


200 000 


ISO  OOO 


50  OOO 


O 226 


> 

T 

,27 

C 

/23  C 

Unit-  Stress  in  5hrruc 

13.  /// 

1 

1,  — 

20000  lb. par  /n. 

22,3-2  E. 


\ 


c-C'k  esj> 


if 

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I \ 


4 


t- 

i 


■e. 


V 

4 

O!  6 


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t 

si 


1 


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OUti  00?, 


s->  OGGQS! 
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00601 


4 

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■0 

do0 


\ 

V N 

\>  '■•», 

\ X 


V 


C <<•  A ; . \ , • '•'>  o 


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9 

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«. 


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\ 


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go;  . c.i. 


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% 


h 


X 


\ 


Si 


\ 


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4 4 


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i \\ 


6 


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\ 


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\ 


6 

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\ 


\V.  •no,  ..v,  - ijtf  X-vv  T'vfr'.,  > 'V.c.Vi 

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b 


. 


y QOO'OG. 


,-\ 

£>.'•  o. 


V- 5^^  VO  ' >C'<oy, 


141 

. 

2000 oo  O O O 

Isooo o / I I 1 

§ / / f f 

K / 
fOflooo  9 V y 9 

; / 

-i  \ / 

§699  f 

f 

o / 

ioooo  1 / 

6 o <>  0 

1 

O 6 36  1 37  i3S  <£39  c 

(40 

1 

i)  56 

< 

,57 

£ 58 

5 59  < 

1 6o 

Uoth&ress  m c 

'S-f'/rruD 

■V. 

/ /n. 

= 20000 

/h 

5(7.  /2 

■ l / 

22,3-2  E 


Itt  <SC 


ISO,  V.  . .. ■ 


■ v\\  czv^L^sy  * 


S -E,.SS 


Unit  Stress  in  Thousands  of  Pounds. 


N 


?,<$:  COCiOOSv 


\ 


\ 


' O'  ~ 


:-e  0 0 003  i 


\ - 
\ 


y \ 

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•r-d ! oooeoi 


\ 


\ 

\ 


CM- 


ct 


f 


O ~<T 


.lii  OOOOT 


V 


■as 

os 

"ai 

C! 


0 

^ - 


S ' “'"O — 

Kfi ! 0 00  33  c. 


■r 


0 


4 


-0  o£! , . •;■•'• 


OSS'S, 


w 


..3  y - <* 

^ ./ -r^4  •’  ,-J  . V'A  t!;,;  D'"-  5 \ • °^'  0 

oA/  > /';  *:  0 U \ *\  O 


o 

r’ 


■r;>  .: /of' 


I 

/fl 

w 

>< 


O. 


£ 

2 


2- 


a 

ov- 

er' 


£ 


OtO  Co,;.,  ..,  iU  .{•  VO 


Unifytnzss  in  Thousands  of  Pounds. 


30 


20 


10 


200  0 00  lbs. 


20 


10 


|50  0 O O lbs. 


to 


105000  ib^. 


10 


TO  OOP  Ib5. 


35000  lbs 


W.  224-i  U.L  22  0 500  lbs. 


p * 


X 


/ * 

M \ 

! 4-  / \ 

' / / \ 

. \ w 

• y / " ' . v.  \ 

' / v ; 

'-5 


v./ 


wa 

A 


•*J!  OOO  0.0$, 


i ■■'■/' \ \ ■ 

K / A \ \\ 

•\  • /.  * \ V 

V'*"  v \ \\ 


^x  \ 


0£ 


OS 


0; 


■ 

v .K 

OS 

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.'/■  \ 

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. 

■<  /v  \\ 

Of 

■■  . - .At 

xv:  ■ - 4 

■«RJ!  1)00.0?! 

f s / ^ V,X  \\ 

^ \/  \ N 

0 

4 

^ ' ~ 


t •: 


^4 


0 0 QgO! 


•=. 


01 

0 

o; 


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CV*  ' — i..  .^1 

•:-V—  ■ 


• ••<!;  > ‘ • C O’ 


. L ..  - '■j/ldJL 


• • - . 


- — -,\- 


& 


0 0 o 

c*'j  <>*•■’ 

V-  f.  ■:  , -J  "- 


' ' ' X «/ 


■/  ?• 

*2  ' '■'*'/  -4,  ; 

yO  ' C •'  -a 


£•-  S/c  v o 0' 


0$ 


' i 


£di  00 e 0 C‘S 


•i-4'  ao  'A' 


0 

<}  O 

0 

C 5 

r, 

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\ 0 

0 0 

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•.  45  'P  , 

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c0  0 *• 

■ ,4  CH*,) 

"S.JJ 

t*  ■ 


"X" 


X>5*Q.Z  V V^^V353kV\^>. 


Load  /n  pounds 


144 


22,4-1  W 


A A 


0 

/ 

j ! : 


, : t \ 

e«;i  xi, 


ip  l. 


c 


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9 v'  ••: 

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u 

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? 


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\ 


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a c. 

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\ ' 


W 


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'U  V ^ v v.j  - V 


14! 


200 oco 


l5ooo 


iSoooo 


Unit  iSfre.55  /n  ^hrrupz.  /in.  =.20000  /t?s. 


2Z,  4-1  W. 


C- 


A 


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> "X;  ■■ 


\ \ 

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\ 


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M M M <5^/ 


<• 


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\ 

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ail 


> 


Si 


/ 


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C • ;J  iu  NJ  O 


\ 


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t 


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Q o 


.»*-  '■o.i  • 

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: 1 

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9 


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\ 

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6 

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f 


• .oS  • ••  7.ryyvv.Vc  ' . G7^v:U  AV. 


I " r-  "-U 


Unit  direjs  in  Tfnouzando  of  Voundo 


3£ 


Un/f~J7re3s  in  Thousands  of  Founds 


Load  tn  Thou  jo  no  of  fLu/ido . 


148 


22,4-1  E*. 


1' 


U/iif  /h  ^yfr'rrupz  /,*.= 20000 /&?. 


22..4--\  E, 


(Snif'Cflresz  in  Uiousannin  of  Fbunc/n 


j Qpuncy_  jo  QpuoQnoqi  u/  zzvjjp  pup 


Ldac/ m "Thousands'  of  Pounds- 


15 


Unit  5fr<zss  in  Ptirrups  /,n  = 20000  /^. 

Z2.f-Z  w. 


\ J.. 


\ 


\ 


<■ 


;o 


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<? 

S'?,  i 


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v 


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si 


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P UO( 


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> 


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c8  i -kg*  c?  o SS<i 


co 


\ 


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\ 


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\ 


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\ 


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es.;  R>.i  Ptvo  ss 

<a  v --  CAox:  ;\L  V\\  OP':,  vX--  ' X\V 


? 


9 001 

I Qcj. 

1 

a « 


.0  a-x.  xs 


\ ,:v' v.  . ''-v  X'v  c;.  \..c • X\r 


Load /h  Jfiousando  of  Pouncio. 


200 


150 


jOO 


50 


O J3 1 1 32 


/ 

/ 

1 

j 

> 

{ 

> j 

s 61 

k62.  J 

, 63  1 

Zoo 


51  6 52  i 53  TS 


U/iif  Jfnzos  in  dtirru/03.  /in . = 20  ooo/fe. 


22,4-2,  w. 


Un if  Sires ^ in  Thousands  oT  Pounds. 


\v.V:vrVy\J^  ^ \vv  y3f^: 


Unit  Stress  in  Thousands  of  Sounds 


tr 


i 


)y 

1 


A,  ■■  A 

•x  - 

'7  -4  //.*. 

» ' -V.  . 

K W--  •> 


A '"\ 


idi  ofjooos 


VO!  u o O Odi 


* / 


\ M 

/'  \ "V 
V »\\ 


-A 


f \ 

A- 


A 

: a 


3£ 


00 


•">1 


•4> 

f--3- 


Oi 


'.‘A- 


lid!  c '.;  CAe  01 


-vis-i ' 


Ql 


■ail  O C O OT 


-•of  ,0  A o \\  r 


- L_  ... 

o • 1 c; 

0 

G 

rj<-; 

o*s  „ o 
r < "c* 

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V ' •• 

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£ 

O 


.;5: 


, .,  / - ;/■/  7 71  . ) '/  w v' 

Y "a-  X /'  > 4 . V!-  v 7 i 


*5 

> 4 


CQ* . a '•  *'  • " 4 .■  • -a  ' . . ri 

■LiiMlAjjJijM, 


;>^\\-  ^%q.o.  \\s  acy-vx  CA  A-  'V,;o 


Load  in  Idousands  of  Pounds. 


200 


1 50 


(OO  9 


SO 


J 6 It  i 


200 


l 9 7 ^ 98 


i |O0 

» 

< 

,20 

28  ^29 

Z//7/74  in  Liirupj  //n  = 2o  ooo  /I5 


22-4-2.  E. 


0 


\ 


X 


o 


k 


f 


OC  \ 


p 6 c 

ee 89  * Ye  i 


A 


\ 


V. 


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h 

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0 '•• 


1 

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X 


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0<U 


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€?  i 8 i 


m 


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Or 


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U-. 

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X 

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X. 

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? 00  lC 

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di  o !..  £_ 


\ 


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\ 


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\ 


\ 


0. 

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X 


\ \ 

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\ 'V  ’ 


V 


\ 

f 

f 


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9 

; 

9 


as  J 


.,  \ P •; 


P.'Vo  . 8*.'  • 'T.|  d:r  i 

ooo  os  v.  \ -■  S\\  o' XX  %0\ 


as 


\ 


002 


oei 


o 00| 


as.*  o 


Load  in  Jhousanc/s  of  Tbunds. 


2oo 


150  A 


i oo<» 


5o 


36  1 37  1 33 


Zoo 


ISO 


100 


j 39  < 

/ 40 

/ 

157 


66 


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Unit  Trass  in  dh'rrups.  /;»  = 20  000  /^. 


22  ,4-2 

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Unit  dfrcss  in  Wousonds  of  Pounds 


Unit'  Stress  in  IPousands  oi  Pounc/s. 


Y\\  V r/'V,N. 


l_o&c/  /n  TfiouSjprtdj  of  f&vnc/o. 


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Load in  Thousands  of  Fbnndj. 


161 


Unit  Sire  jot  in  Tdirrupa . f/n  = 20(joo/6^> . 


Unit  iJfrooo  in  Ifouoandy  of  Vo  undo 


Unit'  Pfross  in  Thousands  oi  Pounds. 


f ..  V. 

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Load  in  TFTouoands  of  Pounds. 


Load  in  Pousands  of  Pounds. 


— i— ! < » 

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Unit Jtross  in  Thousands  ot  "Pounds. 


33. 


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1$7 


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20 

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150000  lbs. 


05  0 00  lt?J. 


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35000  lbs 


22,5-2  UL.ZI4950  lbs. 


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Load  in  Thousands  oT  fdurtdj. 


Un/'f  J fre^o  //?  Thousands  of  T^ound^ 


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Unit  Stress  in  Thousands  of  Founds. 


171 

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150000  lb-3. 


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Load  in  ITFot/sanc/j  of  Pour? cty. 


£2,5-2  E. 


Loads  /n  TJwc/jtfnd^  of  fdundj. 


17 


22,5-2.  Ef 


Unit  J Tress  in  Thousands  of  Vo  undo 


Unit 'Stress  in  TFiousa  ndo  of  T^ounds 


1 Vi 


30 


20 


10 


200000  \Y>5- 


20 


10 


15  0 0 0 0 1175. 


10 

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to 


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70  0 0 0 lt?5. 


5 

0 


35  0 00  lbs 


W.  22.6-1  U.L.  262340  Ita. 


Lonni  /n  Thousands  of  TUnnUs 


176 


200 


ISO 


too 


5 0 


0 

1*23  \24-  i 

1 25  0 63  1 64  i ft  S 

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Unit  Cttr<zxx  in  fyfirr/ /nx  / m = 2000a  its 

22, (2-1  W 

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load  fn  Thousands  of  Tfonda 


2°o  a-  _ 

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Unit  d/reoo  in  df/'rru 

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22,  6-1  W. 


UftifSiress in  Pounds  of  Pounds . 


/ 


/ 


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cr 


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Unif  JVresj  in  Thousands  of  do  undo. 


17‘- 


30 


20 


ZOO  OOO  lbs. 


20 


50  00  0 \b 5. 


io 


1050  OO  lbs. 


10 


0 


70  O OO  lb?. 


35  0 0 0 lb?. 


C 

160 

E.  22,6-1,  U.L.262  34-0  lb? 


•:v  e 


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r.dt  <>•  r-c  '£  dS  • J }J  .!-<!) S.  . Vi 


IN:G' 

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Load  /h  Thousands  of  founds. 


Unit  hfress  in  Stirrups  f /'n.  -20  OOO  IbS. 
22,6-1  E. 


081 


\ 

* 


f 

t-';  A 8 c o i o 


\ 


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ooo 


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Load  in  Jfiousando  of  TbundJ 


181 


22,6-1  E. 


181 


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cpUnOcl  fO  ZpUOQDOLlL  UJ  4! up 


Un if'  Stress  in  Thousands  of  Tbunds. 


Load  in  TiTounandn  of  Tdunds 


2o  o 


15  0 


loo 


50 


200 


150 


100 


50 


00 

r i 

18< 


C.O  u 

f 

15  0 

/ 

j 

/ 0 0 . 

/ 

i"0 

23  124 


63 


64  }>  65 


Unit  J/rkjj  in  df irrupt.  /in.  = 20  000  /bs. 


22,6-2  w. 


Load  in  Thousands  offbunds 


£00  p D 

/ / 

/5  0 1/1 

100  9 9 9 

50  / / \ 

0 1 3 3 i 34  \>  35 

,53 

,54 

55 

A 

V 

Unit  Stress  in  Stirrups.  / in ,—2oooo  /bo. 


2.2,  6 -2  W. 


Unit  Jtreos  in  Thousands  oT  Founds. 


Un/'fyfrz55  in  Thousands  of  Pounds 


zoo 

15  0 

/O  0 

so 

0 

20  0 

15  0 

/OO 

SO 

o 

200 

/SO 

/ 0 0 

50 

0 


188 


8 \ 3 V,  10 


Unit  stress  in 

Stirrups 

! m.- 

fujtffljMjt  ! i 1 1 

22,6-2 

E. 

Load  in  Thousands  of  Fdunds. 


189 

20  o 

/ C f) 

to  0 

5 o 


38 


39  \ 40 


58  J59  dO 


Unit  Stress  in  Of/rrupo  / in  = 2o  ooo  it&. 


22,6-2 


Un/f  ddreoo'jn  TFiou sands  of  Toon c/o. 


Un/f  dines j in  Thousands  of  founds 


191 


30 


20 


10 


200  0 00  lbs. 


2o 


10 


50  OOO  lbs 


10 

O 

10 


05  0 00  lbs. 


o 

5 

O 


TOO  on  ibs. 


550  00  lbs 


W 22.7-1  UL,  261300  |bs. 


20  0 

/5  0 

10  0 

SO 

o 

2oo 

150 

/ 0 0 

50 

0 

20  0 

/5  0 

10  0 

SO 

0 


19 


22-7- 1 W 


20  0 

15  0 

10  0 

5 O 

o 

20  0 

150 

/OO 

50 

0 


22,7-1  VV 


Un/T  Sfrass  in  Thousands  oT  Pounds. 


Unit  Ptress  in  thousands  of  Pounds 


30 


20 


IO 


20  0 0 00  Jfc>. 


20 


10 


o 


I50O00  Ibi 


IO 


o 


0 50  QO\bs 


10 


o 


TO  OOP  lbs 


5. 

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35QOO  lbs 


T 


T 


22,7-1.  U.L  26 1 300  ibj. 


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2.0  o 

IS  0 

10  0 

50 

0 

200 

150 

10  o 

50 

0 


197 


Unit  Jfmsj  in  Stirrups.  /m  =20000 


227-1 

E. 

UnifJfrz^ j m TF)oU,jando  of  Pounds. 


, ,J  r 


.y<»1  GOO  GO' 


--o  ■ " 


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.dCSiOC'C  ./PJ 


GE 


/ 


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rrrr 


Unit'  Utress  in  Tdou^andz  of  do  undo. 


40 


30 


20 


10 


o 


24-0  0 00  [bs. 


20 


10 


200  OOO  Ih3. 


20 


10 


! SO  O 0 O \b3 


10 


'0500 O lbs. 


10 


TO  0 00  I to. 


3S000  lbs. 


W.  22, T- 2 U.L.  2 6S.600  lbs. 


load  In  Thousands  of  Tbunds. 


-tt 


* * '•  V * 


. 


J-Uijii 


Load  in  Thousands  of  Pounds . 


oo^ 


PV  ] 
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\ 

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C C.  v 


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o 


CiO'i 


o<*.\ 


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\ cc\<i  c:-.  •-  asA 


AovvvwC-  r\\  tosrftc- 


:A^W\  <A  v9\  \\NA;? 


Unit-Stress. /n  Thousands  oh  Tbunds. 


liOis 


,c~  — - 


StJL  O O O O-^SL 

✓A, 


X. 


> " ' 


V— 


c,X  ooooos 


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a 

c ^ 

n 

% 

O 

h 

X 

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Unit  J?r<zj<s  in  Jiiouzanafs  of  PounPj. 


30 


20 


10 


o 


240000  lbs. 


20 


10 


zoo  ooo  ibs. 


20 


10 


o 5 


15  0 0 O O 1(75. 


10 


1050 O O 1 1>3 . 


10 


TO  OOO  |bJ. 


3 5000  tbs. 


E.  22.7-2  U.L.  26  8 


' 


; • > 

"/  ■ \ V V 


fit 


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. •*. 


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& 

5 

a. 


C'i 

p 


c 

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• 

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JM)Oa  Oj:  si  O r.JSS. . .3 


Load  in  Thousands  of  bounds 


Unit  stress  in  J tirrupz. 

On.  =2oooo  tbs 

22,7-2-  E. 


00 1 


* i 

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* 

i 

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V.  ” . '0  c- 


ZQ\\rWt C vVv -07/^7, '^v> 


'^c-v\  v,\  o\„  vpm^o; 


Load  in  Thousands  of  Pounds. 


22.7-2 

? E. 

0 0's 


rC •- ; a \v,  Vw'V.v vr •- f.  v ;o : ■ v\ -X' 


Un/fCyfress  in  Thousands  of  Poundo 


fn  Jdou-oando  of  7-b undo 


. 


Load  in  Thousands  of  Pounds. 


.■cJ 


i 


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f 


3 • 


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\'-y  \\yo«ro^viv-;,  7.  o\  'cpr\\^ 


Load  /n  IPousanduoL  Pounds. 


22.8-1  w. 


OZ'i 


A3 


n l 


\ 


\ 


i ?.:•  ; 


COS 


02.: 


OOi 


02 


OOOOS  = cvi\ 


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\g)W^  ^\\^vi^o 


Un/f  JTress  in  Thousands  oT  Po  unds. 


Unit  JYrczs  in  Thousands  of  doundo 


" 


■ 


O)  000  cOi 


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Of 


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10  0 

50 

0 

250 

200 

150 

100 

50 

0 

250 

200 

150 

100 

50 

0 


V \v,  ; vf.-> 


Load  in  Thousands  of  Pounds 


13 


Unit  S tress'  in  Stirrups.  / m - 20  000  It &3. 


22.6-1  E. 


Un/t-Jfr<Z55  /n  Tfiou^andz  of  Pouncfj 


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bis;. 


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Load  /h  Thousands  of  Pounds. 


Unit  Litres s in  dtirrupo  /^  = 20000  /b*. 

22,8-2  w. 


Z oad in  Thousands  of  Pounds. 


22,8-2  VY. 


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Unif  drfress  in  Thou^a  nds  of  Vound^. 


Unit  J Jress  in  Thousands  of  Pounds. 


to 

(2.0) 


220 


260000  lbs 


f|0> 


20 

10 

o 

240000  lbs. 


200  000  lbs. 


20 


10 


150  OOO  lbs- 


10 


0 5 OOO  lbs 


10 


TO  OOO  lbs. 


5 

o 


35000  lbs. 


E.  22.3-2  U.L. 260.000  lbs 


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Load  in  Thousands  of  Fbundo 


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Unit'  Jiress  in  Thousands  of  'Pounds. 


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Summary 


Beam 

No. 

Section 

V6rie-ly 

Age 

Maximum 

Load 

pounds 

6 X/2  /n. 

Culindcr 

Tesfj 

Un  if  load 
pounds 

3+irrup5. 

At  +he  Load  of  200  ooo  lbs 
Maximum  grosses  in  5+irrups. 

3hear- 

ingjtifcss 

tfie^Ul-H. 

Load 

Ib/inz 

Manner 

o-f 

Failure 

vSpdt 

mg 

in 

5T 

Section- 

al 

m* 

Jurfa  ce 
/wa 

m2 

Calculat- 
ed Un<f~ 
5-fra.SS 

Observed  Unif  Stresses 

Observted  Unit  Trusses 
Calculated  Un'ii  3lrtf  xses 

N.W. 

' N.£ 

5.W 

S.E. 

N.W. 

M.E. 

3.W. 

5.E\ 

22.1-1 

VcchnquU 

Wrftouf 

hooks'i.sfirrups 

61 

154  I0O 

4076 

• 

5 52 

D.T 

-2 

IT 

!• 

/l 

6l 

150  000 

3696 

53S 

O 

2 2,2-1 

ft 

W i-Hioot 
stirrups 

6o 

1 67.3.00 

45  22 

S69 

E}r<zak'Vl‘\ 

— 79  J 

Shia*' 

-2 

n 

39 

125  000 

4337 

4S9 

'/ 

22.3-1 

3ti  rrupj 
4"  spacing 

60 

214  550 

4124 

4 

3/s 

.1104 

1.178 

S2  ooo 

3o  ooo 

3/  ooo 

34  OOO 

32000 

.577 

.5^4 

.654 

61S 

760 

T 

-2 

// 

// 

61 

218000 

3689 

it 

35  500 

3o  ooo 

25  50o 

32000 

.630 

.577 

.497 

.6  (S 

.7*1 

22.4-1 

// 

3+iVrups 

T'’5pac.inq 

62 

220500 

41  06 

7 

J* 

.1967 

1.571 

5l4oo 

3o  ooo 

26ooo 

32  0 00 

23  ooo 

.ssC> 

.507 

(,23 

.546 

790 

•/ 

-2 

61 

218000 

3790 

1# 

•1 

St 

30  ooo 

27  nan 

34000 

29  000 

S3  6 

.526 

603 

.566 

7SI 

*t 

2 25-1 

ft 

v5firrup5 
1 I'Spacinq 

62 

229  300 

3788 

II 

Vs 

3067 

1.963 

5l4oo 

30  ooo 

27  000 

23  ooo 

24000 

.532 

.524 

447 

466 

$22 

*/ 

-2 

// 

r 3 

ft 

61 

f j 

214  500 

4041 

it 

31  Ooo 

2 8 ooo 

2&ooo 

2700c 

.603 

54-4 

.544 

.524 

769 

•/ 

22.6-1 

T-shaped 

Ofirrups 

4",5pacinq 

62 

262340 

4 037 

4 

Vs 

.1  104 

M78 

4s  Soo 

32  Soo 

3o  duo 

27  OOO 

30  ooo 

.671 

.619 

557 

>19 

940 

-2 

n 

f J 

6o 

245300 

4331 

n 

U 

31  Ooo 

26  ooo 

28000 

3f  ooo 

439 

.5  3 6 

.578 

.641 

390 

fearing 

Fa.'lur<t 

22,7-1 

n 

Chirrups 

T "Spacing 

62 

261  3oo 

3 799 

7 

Yz 

.1967 

1.571 

47  9 06 

35ooo 

33  ooo 

25  OOO 

30  OOO 

734 

t C9  2 

.5  28 

.Sis 

937 

T 

-2 

n 

// 

60 

268  600 

4346 

tt 

„ 

1/ 

3looo 

32  500 

23000 

3o  5o0 

.4  5 0 

.6  “51 

.4*53 

.640 

963 

ft 

22.5-1 

n 

v5+irrup5 
1 1 "xSpaciruj 

62 

264200 

4058 

1 1 

% 

3067 

1963 

47  8 oo 

24$  ° ° 

23  000 

31  ooo 

29  ooo 

.5  (4 

.449 

.397 

ioO$> 

94$ 

rt 

'2 

h 

// 

60 

26o  ooo 

4152 

0 

n 

23  ooo 

2 3 ooo 

29  5oo 

33  ooo 

,£p  0 (? 

.416 

481 

(o30 

932 

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22.  9-1 

’J&dranqulor 

j3en+up 

.Bars 

62 

225400 

3931 

'j 

-2 

// 

n 

60 

213  700 

4203 

766 

'r 

o>oa 


SZ/A 


% 


4:< 


7 
/ 

#9 


